# User talk:Trovatore

**Previous discussions:**

- Archive 1 (1 July 2005 to 13 October 2005):
- Archive 2 (17 October 2005 to 14 February 2006):
- Archive 3 (12 February 2006 to 4 December 2006):
- Archive 4 (5 December 2006 to 13 June 2011, except one thread):

## Contents

- 1 CH
- 2 Re: LivingBot edit summaries
- 3 Your indent style
- 4 Boiled Lamb?
- 5 Julius Caesar
- 6 Logicism
- 7 Supposition on evenness of zero misunderstanding
- 8 Infinite Dimensional Spaces
- 9 capitalization
- 10 August 2009
- 11 File:Unif small.jpg listed for deletion
- 12 File:Unif.png listed for deletion
- 13 re: Edit at refdesk
- 14 Real zero and integer zero
- 15 Reply +
- 16 Reply
- 17 Over-linking, under-linking, and just-right-linking
- 18 Ch and ON != OR
- 19 New Page Patrol survey
- 20 Another editor correcting your erroneous postings on Ref Desk
- 21 Physical Turing machines are at best a metaphor
- 22 Transfinite induction
- 23 Typesetting Mathematics
- 24 Enumerative combinatorics article
- 25 San Francisco meetup at WMF headquarters
- 26 The car's boot???
- 27 Stefan–Boltzmann law qn in ref desk
- 28 Mary Surratt
- 29 Nomination of Tautology (rhetoric) for deletion
- 30 File:WPMozillaBug.png listed for deletion
- 31 Impossible colors
- 32 Well-founded relation
- 33 I saw your recent edit
- 34 new comment on an archived question
- 35 Misc
- 36 Category:Belgian inventions at WP:AN
- 37 Vesalius
- 38 Cardinal number - History section
- 39 Interlanguage wikipedia link within artile discussion
- 40 RE: captain discussion
- 41 Isaac B. Desha
- 42 'Schematic'
- 43 AC and Group Structure
- 44 Back to the Incompleteness of Arithmetic
- 45 Monty Hall problem RFC
- 46 The infinite
- 47 The Unanswered Question
- 48 Other varieties of English
- 49 I modified my comment after you made yours re "Third realm"
- 50 Cardinal numbers
- 51 I was wondering if this is legit
- 52 Absolutely abnormal number
- 53 Talkback
- 54 Spacing in contractions, esp Italian
- 55 Talkback
- 56 Wikipedia:Reference_desk/Archives/Mathematics/2012_November_20#Guide_to_pronouncing_.28saying.29_mathematics_in_German
- 57 Am I confused as to what Harvard citations are?
- 58 Your revision today
- 59 Thank You From a Necromancer
- 60 File:MixedFontBadness.png missing description details
- 61 Talkback
- 62 Redirects
- 63 Invitation to take a short survey about communication and efficiency of WikiProjects for my research
- 64 Misclick
- 65 Neutron star, black holes on ref desk
- 66 Its'
- 67 Individualism, recent edits.
- 68 advice
- 69 Not a math journal
- 70 Ice Hockey
- 71 Godel
- 72 Ron Paul
- 73 UPDATING AN AGED PICTURE
- 74 Andy
- 75 Compact space
- 76 topoligical
- 77 Removal of the trajectory section in Exponentiation
- 78 Confusing leads in field hockey articles.
- 79 Infinity
- 80 Inaccessible cardinal
- 81 Notification of automated file description generation
- 82 Borel σ-algebra

## CH

In response to

*By the way, CH actually *is* an open question.*

Is that really the way people see it? I'm accustomed to it being treated like the parallel postulate: it depends on what you're doing. The 'existence' of hyperbolic space is not a challenge to the parallel postulate any more than the 'existence' of rectangles is to ~(parallel postulate).

I don't think it's generally accepted that either CH or not-CH is inconsistent (indeed, with Cohen's proof, it's not clear in what sense it could be without much of modern set theory falling apart). Are you suggesting a philosophical position?

(Not an attack, just curious.)

CRGreathouse (t | c) 01:15, 11 June 2011 (UTC)

- My philosophical position is that there is no clear line between philosophy and mathematics (or between mathematics and science), so sure, you can call it a philosophical position if you like.
- Of course there are models of ZFC satisfying CH, and others satisfying ~CH; up to here you're fine.
- But you know, there are also models of ZFC satisfying Con(ZFC), and others satisfying ~Con(ZFC), and we don't treat
*those*on an equal basis. We think Con(ZFC) is true (if it isn't, then there aren't any models of ZFC at all), so the models satisfying Con(ZFC) are right, and the other ones are wrong. - Now, you could make a distinction here on the grounds that both CH and ~CH have
*wellfounded*models, whereas all models of ~Con(ZFC) are illfounded (in fact, they're not even ω-models). - But are the opinions of all wellfounded models equally correct? Surely not. For example, there are wellfounded models that think that 0# does not exist. But if it does exist, which seems like the reasonable thing to believe at this point, then those models are wrong.
- I think I'll stop here for the moment; I'm interested to see what you do with the above. --Trovatore (talk) 09:03, 11 June 2011 (UTC)

- Frankly I'm not a fan of Regularity (seems like too much assumption for too little 'bang'), so I'm not convinced by the ill-foundedness of ~Con(ZF) models though it supports my feelings in this matter.
- It just seems like the claim that CH is open relies on either ZF being false or the system under which the question is to be interpreted changing. The former case seems unlikely; the latter seems unrelated to CH itself.
- CRGreathouse (t | c)
- The axiom of foundation (that's the more usual name than "regularity") is really not an assumption at all. All it says is that we're restricting attention to the wellfounded sets. Note that illfounded models still satisfy foundation. That is to say, they
*think*they're wellfounded. They just happen to be wrong about that. - I'm sorry, I don't understand your second paragraph at all. --Trovatore (talk) 22:21, 13 June 2011 (UTC)

- The axiom of foundation (that's the more usual name than "regularity") is really not an assumption at all. All it says is that we're restricting attention to the wellfounded sets. Note that illfounded models still satisfy foundation. That is to say, they

There is one way in which ~Con(ZF) is different from ~CH — if ~Con(ZF) were true, then we could write down an actual proof of a contradiction from ZF, a **complete** finitary object. While the best one can do with CH or ~CH is to construct (small) finitary **fragments** of models of ZFC+CH or of ZFC+~CH. JRSpriggs (talk) 11:44, 14 June 2011 (UTC)

- That's a difference, certainly, but I don't see that it's relevant in context. If you take the position that the truth of statements of set theory is relative to models of ZFC, then you have to come to terms with the fact that there are models of ZFC that disagree on the truth value of Con(ZFC). --Trovatore (talk) 16:15, 14 June 2011 (UTC)

## Re: LivingBot edit summaries

It is a reference to the preceding sentence ("Revert if in doubt.") Say, for example, you're watching the talk page for "Stretcher" (medical apparatus). Now, LivingBot tags it for a book about woodworking. Clearly, what was meant was Stretcher (piece of wood). The comparison with Georgia is used to imply that LivingBot may actually not be wrong, and you should stop and think before reverting it. - Jarry1250 ^{[Weasel? Discuss.]} 22:02, 19 June 2011 (UTC)

## Your indent style

Regarding this change. Your preferred style makes no sense whatsoever. We both replied to the same comment, I replied before you, and you replied after me. Your method is as follows: if someone replies before you, then you insert your reply above their earlier reply with an extra level of indentation. That has two main flaws:

- Your extra level of indentation adds to confusion. (Indent level
*n*is a reply to indent level*n*–1. Using three indents, when there's only a level zero and level one indent means that you are replying to no-one!) - You imply that your comment is somehow more important than other people's by "cutting in line".

Why should you insert your reply above mine? I replied first, you replied second, ergo, my reply is placed before yours. Following your reasoning, the person to reply after you, i.e. third, should put their reply above both mine and yours, and with an indent level of four (again, replying to no-one). I'll leave you to think about this. Even though you prefer your anachronistic style, it goes against WP:INDENT, and it's quite simply rude. — * Fly by Night* (talk) 05:46, 10 July 2011 (UTC)

- Come on, FBN, you're making way too much of this. I'm not going to apologize because I don't think I did anything wrong. But I am distressed that it strikes you this way, which I never intended.
- To my eye, responses to the same person, indented the same, have a tendency to blend together; the first person's comments get attributed to the second person. I don't have a fixed "style" to solve this problem, but deal with it ad hoc, either with the way I did it, or sometimes by putting an extra newline before my comment. It's silly to extrapolate what would happen if it were iterated; common sense comes into play. --Trovatore (talk) 07:07, 10 July 2011 (UTC)

## Boiled Lamb?

In the discussion on Wholemeal starchy food you refer to boiled lamb with mint jelly as, I think, an English food. I'm intrigued and have never come across any method of cooking lamb that involved boiling it. Are you sure you're not thinking of roasted lamb? I'm asking here rather than extend an off-topic conversation on the refdesk. Thanks. --Frumpo (talk) 08:33, 25 July 2011 (UTC)

- Could be roasted, don't know. --Trovatore (talk) 10:01, 25 July 2011 (UTC)
- The old testament of the Bible mentions "
*You shall not boil a young goat in its mother’s milk.*" in Deuteronomy 14:21. I presume that this would not have been mentioned unless that method of preparation was common-place back then. JRSpriggs (talk) 10:46, 25 July 2011 (UTC) - I suppose a lamb stew (typically with carrots and other vegetables) is sort-of boiled lamb but this wouldn't be normally served with mint sauce. Mint sauce (with a vinegar base) is traditionally served with slices of roast lamb. I haven't seen the sweeter mint jelly for several years. I don't much fancy the idea of lamb boiled in milk but it sounds like an interesting preparation. --Frumpo (talk) 20:52, 25 July 2011 (UTC)

- The old testament of the Bible mentions "

## Julius Caesar

I've seen many interesting opinions on the chap, but never that he was a "thug".

What makes you think that of him? --Dweller (talk) 09:09, 28 July 2011 (UTC)

- He took over Rome by military force, and installed himself as military dictator. I don't know what else you need. --Trovatore (talk) 09:36, 28 July 2011 (UTC)
- Dictator in those days doesn't quite mean the same as these. You can't divorce Caesar from the times he lived in... the traditional senatorial system of the Republic was falling apart and someone had to get a grip. It was him, though not for long. if he hadn't, one of the other triumvirs (or someone else) would have dealt with him rather unfavourably. And what followed him was a path into far greater dissolution of senatorial power. I don't think there's much thuggish about his behaviour though - he believed in the rule of law. To me, he comes across as a powerful man, who was a masterful general, perhaps the most masterful of all time, who couldn't quite make the leap to the imperium. His mistake was that he alienated people and perhaps wasn't thuggish enough to deal with them like a real thug, say Saddam Hussein or Stalin, would have done. --Dweller (talk) 10:10, 28 July 2011 (UTC)
- I am not an expert on the times, but I have a very low opinion of Julius Caesar. I see him as a mob-pandering military ruler, something like the Hugo Chavez of his day (though of course even Chavez in the current day doesn't use the brutal tactics Caesar did). -Trovatore (talk) 10:26, 28 July 2011 (UTC)
- Mob-pandering = popular with the masses? He does seem to have been, but that's not usually a trait of a thug. Caesar's tactics in Rome were spectacularly unbrutal - our article on him notes how he pardoned and spared his opponents. Although he was indeed brutal in warfare against the Gauls and other non-Roman tribes, but you'd expect that of any warrior of his day, and Rome's survival probably depended on it. He also tried to refuse some of the honours the Senate bestowed on him. Give him another look - he's a fascinating and complex character. --Dweller (talk) 11:01, 28 July 2011 (UTC)

- I am not an expert on the times, but I have a very low opinion of Julius Caesar. I see him as a mob-pandering military ruler, something like the Hugo Chavez of his day (though of course even Chavez in the current day doesn't use the brutal tactics Caesar did). -Trovatore (talk) 10:26, 28 July 2011 (UTC)

- Dictator in those days doesn't quite mean the same as these. You can't divorce Caesar from the times he lived in... the traditional senatorial system of the Republic was falling apart and someone had to get a grip. It was him, though not for long. if he hadn't, one of the other triumvirs (or someone else) would have dealt with him rather unfavourably. And what followed him was a path into far greater dissolution of senatorial power. I don't think there's much thuggish about his behaviour though - he believed in the rule of law. To me, he comes across as a powerful man, who was a masterful general, perhaps the most masterful of all time, who couldn't quite make the leap to the imperium. His mistake was that he alienated people and perhaps wasn't thuggish enough to deal with them like a real thug, say Saddam Hussein or Stalin, would have done. --Dweller (talk) 10:10, 28 July 2011 (UTC)

The word "*dictator*" referred originally to an official appointed by the Senate to exercise unlimited powers ("*he was not legally liable for official actions*") for (up to) one year during an emergency. The word got the bad connotation it has today because of the frequent abuse of that power.

Gaius Julius Caesar was a left-wing military dictator, similar to Hugo Chavez as you say. JRSpriggs (talk) 14:20, 28 July 2011 (UTC)

## Logicism

Hi, this may be an odd thing to post, but I don't come around here often and have always found you insightful, so would like to ask your help. The article on Logicism seems to be in a poor state and I don't think the people editing it know what they are talking about (If I'm wrong, I'm very very sorry) Could you take a look at the page (if interested, and if you have time) and give some sort of opinion or indication of a direction it should go in? Finally, I'm the IP address under the small changes section on the talk page there; I'm not asking you to come and agree with/back up what I'm arguing (you may very strongly disagree) all I want is someone who knows what they're talking about to look at it. 71.195.84.120 (talk) 16:16, 31 July 2011 (UTC)

- From pure historical fact, the intro looks very accurate up to the early 1900's. Thereafter (failure of Logicism and Formalism to reduce all of Mathematics to simple Mechanism) there's little info to criticise: article is not inaccurate, just incomplete. Bill Wvbailey (talk) 03:07, 1 August 2011 (UTC)
- What I was looking for comment on was a debate going on on the talk page about two things I removed. The first, refering to Godel's Theorem being an objection to Logicism:
- "However, the basic spirit of logicism remains valid, as that theorem is proved with logic just like other theorems"

- The second:
- "Today, the bulk of modern mathematics is believed to be reducible to a logical foundation using the axioms of Zermelo-Fraenkel set theory (or one of its extensions, such as ZFC), which has no known inconsistencies (although it remains possible that inconsistencies in it may still be discovered). Thus to some extent Dedekind's project was proved viable, but in the process the theory of sets and mappings came to be regarded as transcending pure logic."

- The second removed because, I may be mistaken, I didn't think that mathematics = ZFC was logicism (I'm not asserting this equality) Second, I'm not sure that it is believed that math reduces exactly to ZFC, but more it reduces to Set Theory, which aren't the same. Since what was written didn't seem right, but I wasn't sure exactly what to replace it with, I removed it. I wanted someone else to look at it because some of the comments on the talk page don't seem very informed. I realize that my objections may seem pedantic, but the article seemed to read as pro-logicism to me; and it didn't seem to explain anything about logicism.209.252.235.206 (talk) 03:47, 1 August 2011 (UTC)

- What I was looking for comment on was a debate going on on the talk page about two things I removed. The first, refering to Godel's Theorem being an objection to Logicism:

- Sorry, I didn't have Logicism on my watchlist so I missed the debate. My (historical) take on it is this: Logicism died in ca 1927 2nd edition of PM (see the introduction to that volume), wherein Russell admitted his inability to axiomitize all of mathematics in particular because of the failure of his axiom of reducibility. At this time Hilbert's Formalism, and various "set theories" were in fairly developed stages, and Russell yielded the floor to these theories (with intuitionism a nettlesome bugbear). Russell's axiom was taken up by Goedel in a ca late 1940's important paper, so it's not at all clear that Logicism is strictly "dead". I'm sitting in an airport writing this and when I have more time I'll look deeper at the debate. BillWvbailey (talk) 16:50, 1 August 2011 (UTC)

Walking dead 'eh? First of all, there is a theory called "Neo-logicism" which is thriving just fine. I suppose we could get hyper-semantic and just say something like '...neo-logicism isn't anything like logicism ... it's totally different.' Which is exactly the type of response I expect. However, that would be disingenuous. The idea is that everything in mathematics can be reduced to some logical truth. This claim is eminently reasonable as every mathematician always wants to be logical, and every mathematician always wants to express truths. To the degree that mathematicians run away from logicism, they deserve to lose their credibility. The approach that neo-logicism takes is to expand what we mean by "logic." This, is a perfectly legitimate way to deal with things, and is only at most an equally semantic approach to the approach that the mathematicians are taking in running away from logicism. (Um, who was it who said -- ridiculously -- on a WP talk page that "mathematical logic isn't logic?") Interestingly, the "walking dead" came out with something JUST TODAY.

It's my own person understanding that so-called "philosophical" logicians will always reasonably be able to expand what we mean by "logic" as our knowledge increases. Therefore we will always be able to construct a valid interpretation under which some form of logicism is true. This is their proper role. It is also more properly their role to say whether semantic claims such as "mathematical logic isn't logic" are valid or not. It is not the proper role of a mathematician. Who do you ask about soil, a soil scientist or an archeologist? Greg Bard (talk) 23:04, 1 August 2011 (UTC)

- How is that reasonable exactly? You will always be able to expand what you mean by Logic so that some form of Logicism will be true? Assume I'm stupid and need helped through that because it sounds, to me, like you are saying logic can be what ever you need it to be.
- Now for the other matter: Most of my complaining on the talk page is from pairs of sentences like these:
- "The idea is that everything in mathematics can be reduced to some logical truth. This claim is eminently reasonable as every mathematician always wants to be logical, and every mathematician always wants to express truths."

- Those are not saying the same thing! Saying that all of mathematics (again, the philosophical total form of the word, not just all the math we can do now, but literally everything it can ever be) can be reduced to logic is not the same concept as saying that mathematicians want to be logical in their approach and aspire to truth. You know what? Physicists also want to be logical and aspire to truth, is all of empirical science now also reducible to logic? Obviously not. Just because mathematicians use logic does not mean that everything is logic. 209.252.235.206 (talk) 07:34, 2 August 2011 (UTC)

- The problem is that you are confusing philosophy with psychology. When I say that every mathematician wants to always be "logical," I am not meaning 'spock-like' or some other such notion. I mean it in precisely the sense that the context makes obvious. I.e. the actions of the mathematician when he or she scribbles an expression on the chalkboard are the product of reason. More specifically, there always exists some logical system with some interpretation in which the scribbles can be validly constructed. Yes they
*are*saying the same thing. We are able to expand what we mean by logic in the exact same way that every other academic field does exactly the same thing. We make new discoveries and they are published in academic journals. Do not get the wrong idea. I am not talking about a semantic difference of which academic departments choose to focus on which concepts. I am talking about new discoveries in the field of logic which are consistent with the principles of logic in reality.

- The problem is that you are confusing philosophy with psychology. When I say that every mathematician wants to always be "logical," I am not meaning 'spock-like' or some other such notion. I mean it in precisely the sense that the context makes obvious. I.e. the actions of the mathematician when he or she scribbles an expression on the chalkboard are the product of reason. More specifically, there always exists some logical system with some interpretation in which the scribbles can be validly constructed. Yes they

- I am a little surprised by the issues that you have brought up due to what appears to me to be fairly obvious. Please forgive that. Your counter-example of physics I find to be quite off. Obviously, physics involves an empirical component, while logic does not. Therefore there is no "reducing" all of physics to logic, much less "everything." Math however, does not escape that reduction. The degree to which physics "reduces" to logic is in that the scribblings of a physicist are an interpretation (or model) of the physical world we live in. I.e. they are attempts to formalize the principles of the empirical sciences. The aim of these attempts is to construct a formal system that will produce all of the theoretical possibilities (preferably in the end they are in the form of true sentences) and none of the impossibilities. I don't see how math can escape such a treatment, with the notable exception that math has no empirical component, and therefore reduces to logic just fine.

- I also wonder what the problem is with logic being 'whatever you need it to be.' I am pretty sure Wittgenstein famously described logic as being like a ladder that you can climb and then throw away. We have non-standard logic, non-classical, etcetera. To say that logic is whatever you need it to be also sounds eminently reasonable. Math also appears to be 'whatever you want it to be...' you have graph theory, arithmetic, game theory, topology. Greg Bard (talk) 22:14, 12 August 2011 (UTC)

--

- I'm unfamiliar with "neologicism". I'm only discussing "logicism" here, as it is used in the literature (see the following quotes). Here's what Kleene wrote:

"The logicistic thesis can be questioned finally on the ground that logic already presupposies mathematical ideas in its formulation. In the intuitionistic view, an essential mathematical kernel is contained in the idea of iteration, which must be used e.g. in describing the hierarchy of types or the notion of a deduction from given premises. || Recent work in the logicistic school is that of Quine 1940. A critical but sympathetic discussion of the logicistic order of ideas is given by Goedel 1944." (Kleene 1952:46)

- Here's what Eves wrote (notice that he seems to have borrowed from Kleene !): "Whether or not the logistic thesis has been established seems to be a matter of opinion. Although some accept the program as satisfactory, others have found many objections to it. For one thing the logistic thesis can be questioned on the ground that the systematic development of logic (as of any organized study) presupposes mathematical ideas in its formulation, sucah as the fundamental ideas of iteration that must be used, for example, in describing the theory of types or the idea of deduction from given premises." (Eves 1990:268).

- In the latest Scientific American article there's an article by Mario Livio "Why Math Works" wherein he discusses two -isms only: Formalism and Platonism (August 2011:81) and tries to answer the question about whether mathematics is intrinsic to the universe and discovered by mankind (Platonism), or whether it is Formalistic in nature -- i.e. invented by mankind. He concludes both seem to be the case.

- This brings me to a final thought (opinion) that what we have in this discussion is of confusion between philosophy of mathematics (Formalism and Platonism) and a particular practice of mathematics (Logicism). I personally am sympathetic to the Kleene-Eves point of view (Logicism is a failure) and I agree with Livio who is also a bit perplexed by this universe of ours: "Why are there universal laws of nature at all? Or equivalently: Why is our universe goverened by certain symmetries and by locality? I truly do not know the answers . . ." (p. 83). At least now we have a few quotes from reputable writers to apply to the issue. I'll keep hunting for more. Bill Wvbailey (talk) 13:37, 2 August 2011 (UTC)

- I found a great quote that corroborates my opinion about Logicism being a "practice" rather than a philosophy. This is from Brouwer's 1907
*The Foundations*as quoted by Mancosu 1998:9 -- " 'The Foundations' (B1907) defines "theoretical logic" as an application of mathematics, the result of the "mathematical viewing" of a mathematical record, seeing a certain regularity in the symbolic representation: "People who want to view everything mathematically have done this also with the languarge of mathematics . . .the resulting science is theoretical logic . . . an empirical science and an application of mathematics . . . to be classed under ethnography rather than psychology" (p. 129) || The classacial laws or principles of logic are part of this observed regularity; they are derived from the post factum record of mathematical constructions. To interpret an instance of "lawlike behavior" in a genuine mathematical account as an application of logic or logical principles is "like considering the human body to be an application of the cience of anatomy" (p. 130).

- (But I ask: why do we humans view the universe's apparently regularity? Is it because of an intrinsic "logical" design of our brains?) There's more to be found in Grattain-Guinness:2000 (about 35 cites in his index). Bill Wvbailey (talk) 14:09, 2 August 2011 (UTC)

- To Gregbard: There are some people who purport to be mathematicians or logicians who are not logical. See "synthetic logic", "fuzzy logic", "Paraconsistent logic", and their ilk.
- You said "math has no empirical component". This is false. Mathematics, including logic, is just as empirical as nuclear physics or chemistry. Any calculation or deduction done by a mathematician is actually done in the physical world by some sequence of operations on matter. If these operations did not produce what we consider the proper result, then either that mathematics would not exist or it would be different from what we know it to be. JRSpriggs (talk) 03:57, 13 August 2011 (UTC)

- Aye aye aye. Your characterization of these other mathematicians as "not logical" is just
*your*characterization of them. These people are not setting out to ignore or abandon reason, but rather have constructed a different model of what is reason. Invariably they point to reasons for their constructions. Anyway, the focus should be on the systems, not the people. I think you intend to claim that the*systems of logic*these people construct are "not logical." Like I said this isn't psychology. Whether or not logic is empirical is a very deep and complex subject, and it is not universally agreed that it is empirical. The prevailing view is the opposite. Your appeal to physicalism has my sympathy, as I am a physicalist as well, however physicalism is a metaphysical theory addressing whether or not there is a dualism between mind and matter. The question of whether logic is empirical is not effected by anyone's metaphysical physicalist or idealist views. Empiricism involves being experienced by the senses. Exactly what sense are you using to sense that a particular truth of mathematics is true? It couldn't be sight, after all, a person could conceivably discover all the truths of logic and mathematics sitting alone with eyes closed. <or>I think more properly that like there is evolution in response to the environment, and so too, the evolution of the brain is a response to the 'logical environment' of this universe.</or> As a physicalist, I would say that the 'logical environment' is only experienced through particular instances of activity involving physical matter. However to say that what I am calling the 'logical environment' itself is physical or in anyway directly sensed through the five senses would need some justification and explanation. You only experience it indirectly which makes the "empirical" logic and mathematics of your view only a soft science. Is that your view? That mathematics is empirical, and that it is a soft science? Who is the psychologist now? In my view, we can call things like a "sense of reason", or a "sense of decency" senses, however, they really are a different category of thing than the five senses, and not empirical. Saying that mathematics is done in the physical world does not make mathematics empirical, otherwise astrology, religion, and "noetic science" would also equally be empirical. Greg Bard (talk) 11:25, 13 August 2011 (UTC)

- Aye aye aye. Your characterization of these other mathematicians as "not logical" is just

## Supposition on evenness of zero misunderstanding

Hi Trovatore. As Wikipedia:Reference_desk/Archives/Mathematics/2011 August 10#Is zero really an even number? will soon be archived, I wanted to point out my suppositional response to you question. -- 110.49.248.124 (talk) 15:32, 15 August 2011 (UTC)

- Composite numbers have at least three (but finitely many) non-negative divisors. Prime numbers have two non-negative divisors. One has one non-negative divisor. So in some sense, one is too prime to be merely prime; instead, it is the multiplicative identity. Zero, on the other hand, has an infinite number of non-negative divisors (too composite to be merely composite). JRSpriggs (talk) 23:15, 15 August 2011 (UTC)

## Infinite Dimensional Spaces

Hello Sir. Regarding this question on the maths reference desk. It seems that it's defined the way that it is so that it's a CW complex. You gave a lot of input and really tried to help (which I appreciate), and so I thought you might like to know. All the best. — * Fly by Night* (talk) 01:55, 21 August 2011 (UTC)

## capitalization

If you'll look at the bottom of Wikipedia talk:Manual of Style (capital letters), you'll see that I linked the guideline modification that includes the example "Halley's comet" and mentions astronomical objects. Both Halley's comet and Andromeda galaxy are quite commonly lowercased in sources. I'm attempting to attract a bit more discussion, so just reverting and saying in the edit summary that you missed the discussion isn't all that helpful. Dicklyon (talk) 06:17, 27 August 2011 (UTC)

- I find your recent editing frankly disingenuous. The (talk page) section you mention does not mention celestial bodies at all. You can't take a couple of people vaguely agreeing with a general sentiment as a mandate to impose such a change. Much much worse was that you then, one minute later, used your change as the basis for a requested move at Halley's Comet,
*without mentioning that it was your change*. You really overstepped the line here, badly. --Trovatore (talk) 06:21, 27 August 2011 (UTC)- The change is an attempt to clarify WP's "don't overcapitalize" style. The section is linked in the talk page, and I'm inviting your input there. The RM is already well enough supported by COMMONNAME among other things, since Halley's comet has long been traditionally rendered in lower case, and still is about 50%, as are other well-known comets like comet Hale–Bopp. Dicklyon (talk) 06:39, 27 August 2011 (UTC)
- That may all be true. It's not the point. You didn't discuss the specific change to the celestial bodies section, in specific terms, before making the change. Then, having unilaterally made the change, you used it in support of your position for the requested move.
- That just looks dishonest. I am not saying you personally are a dishonest person, and you may have just been careless about assuming that others had approved the intermediate steps. I can't read your mind; I can see only the edits, and to me they look dishonest, however you may have intended them.
- I haven't contributed on the merits because I have nothing particular to say about the merits. I don't really care whether
*comet*is capitalized or not. --Trovatore (talk) 07:32, 27 August 2011 (UTC)- I certainly wasn't trying to hide anything, but to attract some discussion. The guideline, not necessarily the example that I changed, is what I'm relying on. Dicklyon (talk) 07:40, 27 August 2011 (UTC)
- OK, I can buy that. But surely you must realize that the MoS is full of special cases that may be in tension with general principles. Whether it should be or not, it is. So I'd invite you to be more cautious about making changes to specifics when relying on the generalities, without consensus that they apply and are not covered by an exception.
- As to the specific changes to the "celestial bodies" section, those examples did not make sense anymore after your change. The section said you
*should*capitalize names of celestial bodies, but you changed it to capitalize only the parts that would have been capitalized in any case because of being names of real or fictitious persons. A better example might be the Coal Sack Nebula, however we should or shouldn't capitalize that, a question on which I claim no expertise (though all three words uppercase looks most natural to me, for whatever that's worth). --Trovatore (talk) 08:19, 27 August 2011 (UTC)

- I certainly wasn't trying to hide anything, but to attract some discussion. The guideline, not necessarily the example that I changed, is what I'm relying on. Dicklyon (talk) 07:40, 27 August 2011 (UTC)

- The change is an attempt to clarify WP's "don't overcapitalize" style. The section is linked in the talk page, and I'm inviting your input there. The RM is already well enough supported by COMMONNAME among other things, since Halley's comet has long been traditionally rendered in lower case, and still is about 50%, as are other well-known comets like comet Hale–Bopp. Dicklyon (talk) 06:39, 27 August 2011 (UTC)

## August 2009

You currently appear to be engaged in an edit war according to the reverts you have made on Wikipedia:Manual_of_Style_(capital_letters). Users are expected to collaborate with others and avoid editing disruptively.

In particular, the three-revert rule states that:

**Making more than three reversions on a single page within a 24-hour period is almost always grounds for an immediate block.****Do not edit war even if you believe you are right.**

If you find yourself in an editing dispute, use the article's talk page to discuss controversial changes; work towards a version that represents consensus among editors. You can post a request for help at an appropriate noticeboard or seek dispute resolution. In some cases it may be appropriate to request temporary page protection. If you continue to edit war, you **may be blocked from editing without further notice.** --Enric Naval (talk) 18:33, 27 August 2011 (UTC)

- Enric is a day late (or two years late) and couple of reverts short, since we already stopped reverting and talked about it. Unclear why he decided to be so obnoxious at this point. Dicklyon (talk) 18:39, 27 August 2011 (UTC)

- You'll notice that I made a recent step toward a less controversial version; let me know what you think. Dicklyon (talk) 18:40, 27 August 2011 (UTC)

- Wikipedia:Administrators'_noticeboard/Edit_warring#User:Dicklyon_reported_by_User:Enric_Naval_.28Result:_.29. --Enric Naval (talk) 20:41, 27 August 2011 (UTC)

## File:Unif small.jpg listed for deletion

A file that you uploaded or altered, File:Unif small.jpg, has been listed at Wikipedia:Files for deletion. Please see the **discussion** to see why this is (you may have to search for the title of the image to find its entry), if you are interested in it not being deleted. Thank you. **S****ven Manguard** **Wha?** 03:39, 30 August 2011 (UTC)

## File:Unif.png listed for deletion

A file that you uploaded or altered, File:Unif.png, has been listed at Wikipedia:Files for deletion. Please see the **discussion** to see why this is (you may have to search for the title of the image to find its entry), if you are interested in it not being deleted. Thank you. **S****ven Manguard** **Wha?** 03:40, 30 August 2011 (UTC)

## re: Edit at refdesk

It certainly was an accident. I'm not actually sure how that happened --- your reply didn't exist when I began replying, and I wasn't taken to an edit conflict page as I should have been.--Antendren (talk) 23:15, 16 September 2011 (UTC)

- Yeah, that happens sometimes. Sorry I overreacted. --Trovatore (talk) 00:50, 17 September 2011 (UTC)

## Real zero and integer zero

Hi Trovatore. I am trying to understand your way of doing math. You distinguish between real zero, , and integer zero, . They are 'completely different breeds of cat', so , but when they are together in expressions the may be converted to such that for instance . Do I get it right? The meaning of the power depend on which one of the zeroes is in play in the exponent such that while is an undefined indeterminate form. Right?. Now what about the rational zero ? It is a different breed of cat than and . Right? Is defined to be one or is it undefined? And why? Bo Jacoby (talk) 09:55, 18 September 2011 (UTC).

- Bo, most of the time, I
*don't*distinguish between them, because most of the time there's no reason to. I don't want to waste my time making distinctions when they don't make a difference. - But in contexts where they could make a difference, like the famigerated 0^0 thing, I don't think the claim "they're equal, so you
*can't*make a distinction" is really very convincing. You keep saying what disasters would befall, but you've never given a good example, and indeed the fact that these objects are coded differently into set theory, and yet the sky has not fallen, seems to me a pretty convincing demonstration that there is at least no*simple*disaster that the distinction causes. - As for the rationals, yes, I do think a distinction can still be made. At a sound-bite level, you could say the rationals are inherently algebraic, whereas the reals are inherently topological. As long as you're at the level of algebra, 0^0=1 seems pretty convincing. Add topology and it no longer is. --Trovatore (talk) 23:07, 18 September 2011 (UTC)

JRSpriggs, Thank you for asking. Trovatore and I had a discussion on Talk:Exponentiation and the archives pages such as Talk:Exponentiation/Archive_3#0.5E0 regarding the definition of 0^{0}. Sorry for not being explicit about it here. Bo Jacoby (talk) 02:49, 19 September 2011 (UTC).

Trovatore. To a mathematician a contradiction marks the end of civilization as we know it. As both and satisfy the equation of first degree , and actually any equation of the form , it follows that in contradiction to . This is a *simple* disaster that the distinction causes. The sky has fallen. The various codings of integers and reals in set theory are merely proofs that the defining axioms for reals and integers are consistent. These codings do not *define* reals or integers. The axioms do. Bo Jacoby (talk) 08:19, 19 September 2011 (UTC).

- Axioms do not define anything. Axioms assume that objects behave in a certain way. From those assumptions you prove other things. --Trovatore (talk) 08:33, 19 September 2011 (UTC)
- Now, as to your specific example. The sentence is satisfied by the structure and also by the structure . However that does not tell you anything about how the interpretation of the constant symbol 0 in the first structure sits in the second structure. You cannot conclude that , because you don't know that is in element of the universe of the second structure in the first place. --Trovatore (talk) 08:38, 19 September 2011 (UTC)

What does the *structures* and mean? Bo Jacoby (talk) 16:38, 19 September 2011 (UTC).

- I am sure he means Structure (mathematical logic). Note that, in the usual definitions, is a set of pairs of natural numbers, as is every other integer, while is a set of Cauchy sequences of rationals, and so in particular is not a real number and is not an integer. It is true that there is an embedding of one structure into another, but this embedding is not the identity. This is completely analogous to the situation in a programming language where there is a type Integer and a type Real, and an object of Integer type has to be cast into the Real type before being passed to a function that takes an argument of type Real. — Carl (CBM · talk) 16:58, 19 September 2011 (UTC)

To put it less technically, your equation , as interpreted in the real numbers, doesn't tell you anything except in the case that *x* is a real number. It does not say, for example, that if you add the 0 of the real numbers to me you get back me, because I am not a real number I am a free man. Also, the symbol + is to be interpreted as in the real numbers and there is no guarantee that that has anything to do with the + of any other structure, such as the integers. --Trovatore (talk) 19:12, 19 September 2011 (UTC)

The zeroes in and confuses me. Did you mean and ? Bo Jacoby (talk) 23:34, 19 September 2011 (UTC).

- Structures are specified by a universe and an interpretation. Interpretations tell you how to interpret the constant symbols, function symbols, and relation symbols of the language. Typically, when the
*way*the symbols are to be interpreted is understood from context, you just list*which*symbols you want to interpret. So I listed the constant symbol 0, and the function symbols plus and times. - I could also have listed the constant symbol 1; that would probably have been more standard. On the other hand 1 is definable in both structures so I didn't really need to list it, but the same is true for 0.
- So sure, your suggestion would work, but so would and , and the latter would probably be more standard. --Trovatore (talk) 23:39, 19 September 2011 (UTC)

Thanks to Carl for the link to Structure (mathematical logic) which I find interesting but difficult to understand in detail.

The same structure can be constructed in different ways. The structure of the real numbers was constructed by Cantor and by Dedekind as completely different breeds of cat. Does this mean that is different from ? Or is the important things that they represent different realization of exactly the *same* structure ?

Trovatore said: ' I *don't* distinguish between them, because most of the time there's no reason to. I don't want to waste my time making distinctions when they don't make a difference.' I could not agree more! The undefining of into being an indeterminate form is the only example I know of *undefining* in math. Are there other examples?

(The *order* of the real numbers is not *generalized* into the realm of complex numbers, but that does not mean that the order of reals becomes undefined.)
Bo Jacoby (talk) 13:14, 20 September 2011 (UTC).

## Reply +

I put some stuff for you on my talk page in the section you started, unrelated to the section topic. PPdd (talk) 03:29, 26 September 2011 (UTC)

## Reply

Hello. Just to let you know, in case you don't see it any time soon, that I responded to your last comment, on the Talk page. You can click here. Hashem sfarim (talk) 16:22, 5 October 2011 (UTC)

## Over-linking, under-linking, and just-right-linking

Trovatore, there seems to be a movement afoot to reduce overlinking by making rules to favor links' role as definers of unfamiliar terms and end their role as pointers to different but strongly related topics—for example, saying that a page about a bureau of immigration shouldn't link to Immigration, because everyone knows what immigration is, and Immigration doesn't provide facts of immediate relevance to the bureau. That sounded like progress to me at first, but as I have seen it play out in practice, it has begun to sit ill with me. Would you be willing to have a look at Wikipedia_talk:MOSLINK and see what you think? —Ben Kovitz (talk) 11:41, 16 October 2011 (UTC)

## Ch and ON != OR

These are the same principals... so you were like 1-4 steps from solving CH... that's basically the point of my summary of the proof.

You either chose N_0 to be the first choice, and name the first player 0_R, and the laster player R_e, and then all the information is encoded into the players names and the game... so there is no perfect information since no player knows all the names.

I hope this makes sense to you and you see where I went with it.

-Vince

WhatisFGH (talk) 01:41, 19 October 2011 (UTC)

- You know, when I was a grad student I would take up these arguments, but it's gotten old. Why don't you get onto Usenet and post this to sci.logic? I'm sure there'll be people there who are willing to talk about it. http://groups.google.com/group/sci.logic/topics . --Trovatore (talk) 01:45, 19 October 2011 (UTC)

## New Page Patrol survey

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## Another editor correcting your erroneous postings on Ref Desk

I have opened a discussion thread about the modification of the Ref Desk posts of others at Wikipedia talk:Reference desk#Modifying someone else's post. Your input is most welcome. Edison (talk) 06:50, 16 November 2011 (UTC)

- Trovatore, just thought I'd drop you a note. I really meant no harm with fixing the link that started the above mentioned thread. I hope no offense was taken, none was intended. I really didn't think such a trivial fix would generate this much drama, but I will definitely be keeping it in mind in the future. Regards,
**He****iro**14:08, 16 November 2011 (UTC)

- Trovatore, just thought I'd drop you a note. I really meant no harm with fixing the link that started the above mentioned thread. I hope no offense was taken, none was intended. I really didn't think such a trivial fix would generate this much drama, but I will definitely be keeping it in mind in the future. Regards,

## Physical Turing machines are at best a metaphor

Hi, regarding your posting on the Ref Desk at Wikipedia:Reference desk/Science#Is Wikipedia a conscious entity?, you said that a programmable calculator is not Turing-complete, and that a TM is a mathematical object. Obviously, using a mathematical construct to describe a physical machine is an approximation - namely that physical machines do not have access to the infinite-length-infinite-storage resources of the mathematical structure. Nevertheless, this should be obvious when one talks about physical machines, which was what computational theory was built to address anyway (like why a system of assembly-line beltways, a queue machine, can't handle certain instructions). So unless I'm missing something, I think the statement that calling a programmable computer Turing-complete is "at best a metaphor" is a quite a mischaracterization. Please let me know. SamuelRiv (talk) 22:06, 3 December 2011 (UTC)

- People need to be careful throwing around terms like the Church–Turing thesis, which is a concept from mathematical logic, not from the theory of (physical) computation. I stand by my statement. Turing machines are objects treated in mathematical logic; no real-world machine is a Turing machine, and the concept of "Turing completeness" applies only to the idealization of what the machine is
*supposed*to do; it's a misapplication of the concept to talk about any physical machine*actually*being Turing complete. --Trovatore (talk) 22:55, 3 December 2011 (UTC)

- Except it's useful, if discussed properly. I agree that the previous posts were a bit out there, and one shouldn't throw around vocabulary like Church-Turing (or especially, god forbid, Godel's Incompleteness Theorem) without mathematical reason. But saying something is a Turing-complete is useful, like in the assembly line example I gave. If one wants to put some kind of quality-checking machinery into an assembly line, one has to make sure that if the program is too "complex", one knows to make the necessary adjustments to the architecture.
- It is relevant in the discussion of quantum computers. We do not and will not have infinite qubits, but because we deal with scaling problems, it is often necessary to know what the complexity class of one's architecture would generalize to. It is also relevant in the discussion of neuroscience, mostly to make sure people don't confuse brain complexity with computational complexity.
- So the point is that while I agree that one has to be extremely careful about throwing around mathematics terms (as we are so often reminded in physics), the work of Turing, Church, etc. was inspired to be
*applicable*to the world. A term, then, can be used to make a point with the (hopefully) obvious assumption that it is an abstraction of that term. SamuelRiv (talk) 00:06, 5 December 2011 (UTC)- Well, it's not so much that it's an abstraction of the term, as it is a direct application of the term, but to an idealization of the device. But you have to keep in mind that results that apply to the idealization of the device may not apply to the device itself. This is particularly true for "Turing completeness", which I think is totally out of place to bring in when discussing consciousness. --Trovatore (talk) 00:23, 5 December 2011 (UTC)

- Agree with Trovatore. "Turing completeness" is neither necessary nor sufficient for consciousness. Of this I am 100% certain: consciousness has nothing
*whatever*to do with Turing completeness. While I hold that the squirrels on my deck looking for birdseed*are*in the absolute sense conscious, not a one of them is Turing complete or even a dimly-finite approximation to it -- how many squirrels do you know that can multiply 7 x 5, or even count to three for that matter? Why on earth would a squirrel need to be able to count or multiply? Life and survival and consciousness in this world of ours has nothing whatever to do with Turing completeness, or computation for that matter. Bill Wvbailey (talk) 02:11, 5 December 2011 (UTC) - See Hard problem of consciousness. It's a stub, not an article, really. But the intro gets pretty close to an expression of "the problem". Naively the problem gets its name from the difficulty of "explaining consciousness", but the real source of its moniker is the fact that the
*question/problem itself*is so hard to frame, to grasp, to intuit, to describe/express. Bill Wvbailey (talk) 02:32, 5 December 2011 (UTC)

## Transfinite induction

I've started a discussion on the talk page. I will add the sentence back if you do not respond soon and justify yourself. Thehotelambush (talk) 00:40, 8 December 2011 (UTC)

## Typesetting Mathematics

Hi Trovatore I want to ask you for help with typesetting mathematics. I am attempting to typeset a summation with a multiline subscript (In this particular example its a summation operator with a n=0 subscript and below that n odd). Usually when using LateX I would make use of the \substack command, but Wikipedia can't parse this command for some reason. Do you know how to do this? I thank you in advance for your help. NereusAJ (talk) 02:40, 23 December 2011 (UTC)

- The LaTeX engine used here is kind of restricted. If something doesn't work, in my experience, usually you just have to do without it. In this case I'd suggest just putting the two conditions on one line: . I know it's ugly.
- You could ask Michael Hardy, who sometimes knows more about this stuff. --Trovatore (talk) 03:48, 23 December 2011 (UTC)

## Enumerative combinatorics article

Hi Trovatore. I am busy expanding a stub article on Enumerative combinatorics. I would appreciate your input as I haven't made anything but minor edit so far to Wikipedia. I have added new content to the page and would like your opinion as to my approach. My plans to further expand the article include adding additional examples of combinatorial objects (like Dycke paths, Cayley trees, cycles and permutations) and how these can be enumerated. However, the method for all of them is somewhat similar and I am worried about being repetitive. Thank you. --**NereusAJ (T | C)** 02:57, 5 January 2012 (UTC)

## San Francisco meetup at WMF headquarters

Hi Trovatore,

I just wanted to give you a heads-up about the next wiki-meetup happening in SF. It'll be located at our very own Wikimedia Foundation offices, and we'd love it if some local editors who are new to the meetup scene came and got some free lunch with us :) Please sign up on the meetup page if you're interested in attending, and I hope to see you soon! Maryana (WMF) (talk) 00:31, 10 January 2012 (UTC)

## The car's boot???

Hi, there! It's just not English. Possessive 's is not used for inanimate objects. See Thomson & Martinet, *A Practical English Grammar* 2nd edition (London: OUP, 1976), p. 11, **11**c: "When the possessor is a thing **of** is normally used: the walls of the town ... the legs of the table ... But with many well-known combinations it is usual to put the two nouns together using the first noun as a sort of adjective ... hall door ... dining-room table ... street lamp".

What this means is that it is OK to say "the boot of the car" and OK to say "the car boot", as in the common phrase "car boot sale". But it is absolutely not OK to say "the car's boot". It is a comical error that would be red-pencilled in primary school. That it is uncorrected in the MOS is ... well, unbelievable. Best regards, Justlettersandnumbers (talk) 00:26, 10 February 2012 (UTC)

- I think you're just flat wrong. This is completely standard English. I have never heard of Thomson & Martinet but it must be a very odd book. --Trovatore (talk) 00:36, 10 February 2012 (UTC)
- Let me hazard a guess: you are not a native speaker of British English. That's not a crime. But if the MOS wants an example of how to translate from one idiom to the other, it'd better get both of them right, wouldn't you say? If you don't know that particular – and rather well-known – standard grammar, would you refer me to another grammar of British English that supports your position? Or otherwise consider undoing your reversion of my edit? Justlettersandnumbers (talk) 00:54, 10 February 2012 (UTC)
- Thank you. If people want to spend time looking for a better example, I'm ready & willing to participate. Meanwhile, Evviva Verdi! Justlettersandnumbers (talk) 01:21, 10 February 2012 (UTC)
- You know, I actually don't see anything in the passage you quote that says it's an error to say
*the car's boot*. Depending on the context in which the passage occurs, it may suggest that*the boot of the car*is more usual, but that is a rather different thing. - To me the difference between
*the car boot*and*the car's boot*would be that, in the second form, you have a particular car in mind, whereas when*car*is used appositively it's more explaining what sort of boot it is (for example, that it's not footwear). --Trovatore (talk) 01:46, 10 February 2012 (UTC)

- You know, I actually don't see anything in the passage you quote that says it's an error to say

- Thank you. If people want to spend time looking for a better example, I'm ready & willing to participate. Meanwhile, Evviva Verdi! Justlettersandnumbers (talk) 01:21, 10 February 2012 (UTC)

- Let me hazard a guess: you are not a native speaker of British English. That's not a crime. But if the MOS wants an example of how to translate from one idiom to the other, it'd better get both of them right, wouldn't you say? If you don't know that particular – and rather well-known – standard grammar, would you refer me to another grammar of British English that supports your position? Or otherwise consider undoing your reversion of my edit? Justlettersandnumbers (talk) 00:54, 10 February 2012 (UTC)

Just for reference, a few examples of possessives on inanimate objects in British English: car's car's car's car's car's phone's show's palace's region's century's. — Carl (CBM · talk) 02:05, 10 February 2012 (UTC)

- I can only assume that Thomson & Martinet were trying to apply a particular bugbear of their own: it was certainly not descriptive. Their book's assertion is not in keeping with British English's normal practice. Kevin McE (talk) 07:24, 10 February 2012 (UTC)
- Well, as I said above, I don't even see it in the quote from T&M. It does say that
*of*is "normally" used, an assertion I won't disagree with (even in American English), but that's very different from saying that the possessive form is an error, or even something to be preferentially avoided. --Trovatore (talk) 07:29, 10 February 2012 (UTC)- I don't know of any inhibition against possessives of things in American English, either. I have lots of guides, haven't seen anything like that. In book search, I did find one guide that says use "of", but also says that nowadays its increasingly common to just use the possessive apostrophe. It also has a completely lame example: "pile of coats" as opposed to "coat's pile", which is not a possessive at all so nobody would do that. Like a "coal's lump"? Dicklyon (talk) 08:02, 10 February 2012 (UTC)

- Well, as I said above, I don't even see it in the quote from T&M. It does say that

Hi Trovatore, long time. I should probably not reopen this old thing, but I have the itch. Thomson and Martinet are quite correct to say *But with many well-known combinations it is usual to put the two nouns together using the first noun as a sort of adjective* and economy of language makes this mode of expression attractive - but here it is no longer a possessive but an attributive and this kind of construction is not flexible enough to serve as a general replacement for possessives. For example, consider "The office's east-facing windows" or "the dog's most chewed bone" - the attributive equivalent rearrangement is ungrammatical and the "of" construction does not improve the passage. And the attributive construction also needs to be idiomatic: e.g., the NPs in "through ill-use the trousers suffered three rents and the jacket two" could be referred to again as "the trouser's holes", but "the trouser holes" is unidiomatic, sounding as if they are holes that trousers are expected to have.

This is an example of a poorly understood recommendation being oversimplified and hardened into peevological dogma. I do hope those primary school teachers aren't for real. — *Charles Stewart* (talk) 10:32, 26 October 2012 (UTC)

## Stefan–Boltzmann law qn in ref desk

Can you help me answer things in the "Stefan–Boltzmann law" section in the reference desk? It is above the absolute temperature section.Pendragon5 (talk) 00:22, 12 February 2012 (UTC)

## Mary Surratt

Wow. BusterD (talk) 21:17, 31 March 2012 (UTC)

## Nomination of Tautology (rhetoric) for deletion

A discussion is taking place as to whether the article **Tautology (rhetoric)** is suitable for inclusion in Wikipedia according to Wikipedia's policies and guidelines or whether it should be deleted.

The article will be discussed at Wikipedia:Articles for deletion/Tautology (rhetoric) (2nd nomination) until a consensus is reached, and anyone is welcome to contribute to the discussion. The nomination will explain the policies and guidelines which are of concern. The discussion focuses on good quality evidence, and our policies and guidelines.

Users may edit the article during the discussion, including to improve the article to address concerns raised in the discussion. However, do not remove the article-for-deletion template from the top of the article. **Ten Pound Hammer** • ^{(What did I screw up now?)} 01:11, 1 April 2012 (UTC)

## File:WPMozillaBug.png listed for deletion

A file that you uploaded or altered, File:WPMozillaBug.png, has been listed at Wikipedia:Files for deletion. Please see the **discussion** to see why this is (you may have to search for the title of the image to find its entry), if you are interested in it not being deleted. Thank you. Cloudbound (talk) 21:26, 8 April 2012 (UTC)

## Impossible colors

Trovatore, Your answer about red+green could easily be misinterpreted as "additive and subtractive color mixing are really more or less the same thing, who cares?". Maybe you could expand a little, or clarify, in order not to confuse the IP editor? --NorwegianBlue^{ talk} 06:34, 12 April 2012 (UTC)

## Well-founded relation

~~Some 3 years ago, you had a long discussion on the above page, but somehow, it managed to miss an important point about infinite descending chains. I posted again, at the bottom of the talk page, on this. Perhaps you can clarify. linas (talk) 03:29, 21 April 2012 (UTC)~~

## I saw your recent edit

at a Warren Zevon album (I had made a similar correction elsewhere) and was wondering what you thought of the statement, "**the novelty song "Werewolves of London"**? Is W of L really a novelty song? Einar aka Carptrash (talk) 14:48, 15 May 2012 (UTC)

- Seems borderline. I wouldn't have said so but I can see how someone might think otherwise. But then you could make the same claim about most of Zevon's opus, which seems reductive. --Trovatore (talk) 18:55, 15 May 2012 (UTC)

## new comment on an archived question

Take a look: Wikipedia:Reference_desk/Archives/Computing/2012_May_19#Is_indexing_a_safety_risk.3F — Preceding unsigned comment added by OsmanRF34 (talk • contribs) 20:41, 23 May 2012 (UTC)

## Misc

You may remember me from the AfD discussion,Crimes_involving_radioactive_substances.

Anyway, my dissertation advisor at Stevens just accepted a position at UNT, I think it may even be the Math Department, although his background is in Systems Engineering.

Small world...

Roodog2k (talk) 15:31, 25 May 2012 (UTC)

## Category:Belgian inventions at WP:AN

Hello. This message is being sent to inform you that there is currently a discussion at Wikipedia:Administrators' noticeboard regarding an issue with which you may have been involved. The thread is "Category:Belgian inventions". Thank you. Andy Dingley (talk) 20:38, 12 June 2012 (UTC)

## Vesalius

Hello. I can understand your viewpoint on "De_humani_corporis_fabrica" not being an actual invention as such. How could this be added / mentioned and be a better fit ? Maybe a category Belgian "Discoveries" or Belgian "contributions to sience" ? I also think "inventions" is someone specific as a word , but I would think it is currently used as a term to encompass innovation in general to avoid having too many categories at the bottom of pages. Also if you insist , I could make a subcategory "Flemish Inventions" . I will check this page again for an eventual reply . 3 days ago there was no category "Belgian Inventions" , together with a few others we are in the process of populating it . Vesalius is something we learn at school as being something that originated here , and that's why It was one of the items I thought should be mentioned . Regards 83.101.79.45 (talk) 06:52, 14 June 2012 (UTC)

## Cardinal number - History section

You affirm that the history section of cardinal number article has [sources and citation]. But the whole section does not have any reference nor citation.

I have written a note, but another editor deletes it.

The whole section is awful and must be rewritten. I have written a warning on this, but also it was deleted. Citations and sources justifying correct statements must be added.

The section induces the following misunderstandings:

1) Cantor was the first to consider the one-to-one correspondence as a way of quantity, because previous authors are not cited.

2) Cantor first has formulated the one-to-one correspondence for finite sets and then has extended it for infinite ones.

3) Cantor has given a suitable notion of cardinal number

4) The current notion of cardinal number is essentially the Cantor concept.

Please read: http://en.wikipedia.org/wiki/Wikipedia:Administrators%27_noticeboard/Edit_warring#Edit_warring_in_Cardinal_number

Apologize the bad English

Regards

Carlos --Gonzalcg (talk) 21:48, 23 June 2012 (UTC)

## Interlanguage wikipedia link within artile discussion

Some Chinese Wikipedian told me, English Wikipedia is a improper place to discuss this issue. I closed the discussion and moved to meta. Please continue the discussion in meta.--王小朋友 (talk) 08:17, 30 July 2012 (UTC)

## RE: captain discussion

Template:Wb daintalk 01:03, 24 August 2012 (UTC)

## Isaac B. Desha

Thanks for fixing my foul up in the lead. I wrote it carelessly. Acdixon ^{(talk · contribs)} 19:48, 27 August 2012 (UTC)

## 'Schematic'

Wickid123:
| |

It may be personal, but ideas generally are... Even if that is an issue how then are new things created, and those ideas put forth? I really do think it deserves to be on a science-orientated-page. I doubt I am the first with the idea, but perhaps there is no evidence... So I don't know what to do. Thanks.Wickid123 (talk) 10:27, 12 September 2012 (UTC) |

- You need to find the ideas in what we call a "reliable source". That phrase does not necessarily have quite the meaning you would expect from normal English — see Wikipedia:Identifying reliable sources for more details. We're not allowed to just make stuff up here — even if it happens to be correct. --Trovatore (talk) 00:40, 12 September 2012 (UTC)

## AC and Group Structure

Hi!

I have written a proposal for a new article. It's about the equivalence of AC and the existence of a group structure on every set. It's on my talk page. (It's about the only thing there, so you'll be able to locate it. Lead + two sections + references) I'd like to place it in the AC category if it's good enough, and perhaps link it from the AC article. Perhaps it should be in category Group too.

I think that the first section (Group Structure -> AC) is kind of neat. Well, perhaps not my presentation of it, but the main reasoning, which I think come from the second reference.

I'd be happy if you, Carl and JRSpriggs (and anybody else you feel ought to) could have a look at it. It's not in mint condition yet, but I don't want to spend too many more hours on it in case you all say booooooo. Keep in mind that I am just a layman.

Best Regards, Johan Nystrom YohanN7 (talk) 12:36, 15 September 2012 (UTC)

## Back to the Incompleteness of Arithmetic

Hi, I assume you remember our discussion we had a week ago. I suspect there's still something left I couldn't understand from what you wrote: Is there a proposition - **all of whose quantifiers range over natural numbers only**, which is neither proved nor refuted in Second-order Arithmetic interpreted in **Two-sorted First**-order Logic?

Btw, what you wrote made me understand, that Second-order Arithmetic - interpreted in **Second**-order Logic - is not effective/computable, although it's complete, am I right? Additionally, you wrote "*Second-order logic is extremely powerful (for example it either proves or refutes the continuum hypothesis, assuming, well, basically nothing*)". What do you mean by "nothing"? Even not ZF?

77.127.133.106 (talk) 07:51, 20 September 2012 (UTC)

- If you think you don't know the answer to my question, please say "I don't know", and I will ask at the reference desk. Thanks. 77.127.133.106 (talk) 21:11, 20 September 2012 (UTC)
- No, I can answer it all. You know, these things are really not mysterious — with a few hints you should be able to figure them all out yourself.
- First point: Yes, there is such a proposition. Take for example the proposition "ZFC is consistent". This can be expressed in the form you're asking for, for example
*For every natural number n, n is not the Goedel number of a proof of 0=1 from the axioms of ZFC*.

- That proposition cannot be refuted by second-order arithmetic, because second-order arithmetic proves only true things, and the negation of the proposition is (presumably) false. On the other hand, neither can it be proved by second-order arithmetic, because the proposition implies that second-order arithmetic is consistent, which second-order arithmetic cannot prove.
- Second paragraph — right. Full second-order arithmetic in second-order logic is complete, for the following reason. Given a model of the theory, for any genuine natural number
*n*, it's easy to show that there is a corresponding object in the model, and moreover that this correspondence gives an isomorphic embedding from the genuine natural numbers into the natural numbers of the model. So all we need to know is that*all*natural numbers of the model can be obtained in this way. - But suppose not. Then let
*P*be the predicate that picks out, from the natural numbers of the model, the ones that are obtained from the genuine natural numbers by the canonical embedding. Now apply the induction axiom to*P*. - And for the last point, right, you need much less than ZFC. Just enough to say that sets sort of behave like sets, and possibly the axiom of infinity; I'd have to think about it to see exactly what you need. --Trovatore (talk) 21:22, 20 September 2012 (UTC)
- Thank you for your quick answer (like a missile). Since you didn't refer to the first half of my second point, namely: whether Second order Arithmetic - interpreted in Second-order Logic - is not effective/computable, so I guess it's really not. All the best. 77.127.133.106 (talk) 22:12, 20 September 2012 (UTC)
- Right — if it were computable, you could violate the incompleteness theorem (just take every statement implied by the theory as an axiom). --Trovatore (talk) 23:17, 20 September 2012 (UTC)
- Thanks. Btw, I understand that if Second order Arithmetic - minus Axiom of Induction - is added to Second-order Logic, then Axiom of Induction will be proved-or-refuted in the new system, am I right? If I am, then I understand that - the usual reason for adding Axiom of Induction to such a complete system - is generally just for the sake of convenience, i.e just in order to have more
*computable*proofs for properties of natural numbers, correct? 77.127.133.106 (talk) 23:28, 20 September 2012 (UTC)- No, I don't think that's right. Induction is what "says" that we're talking about the natural numbers. Without induction, I don't see any reason the theory should be categorical. --Trovatore (talk) 23:30, 20 September 2012 (UTC)
- Hence, Second-order Logic is powerful enough for proving-or-refuting the Hypothesis of Continuum, yet not powerful enough for proving-or-refuting Axiom of Induction. Correct? 77.127.133.106 (talk) 00:08, 21 September 2012 (UTC)
- OK, so I overstated the case a
*slightly*when I said SOL decides CH from "basically nothing". You need a*little*bit; enough, at least, to make sense of the question. For example the hereditarily finite sets are a structure for SOL, but it would be bizarre to ask whether CH is true or false in that structure. - But you don't need much. You need an infinite set, and you need the powerset of the powerset of that. You don't need separation, because separation is just true in the logic itself. You don't need choice, you don't need replacement. I'm not interested enough to pick through and decide whether you need union or pairing. Basically you just need enough to guarantee that the model has a referent for all the terms in the question. --Trovatore (talk) 07:35, 21 September 2012 (UTC)
- Because you only need a finite number of axioms, in second-order logic with full semantics you can write a sentence which is satisfiable if and only if CH holds, in the signature that includes only equality. This is the sense in which full semantics decide the truth value of CH. But that sentence is neither
*provable*nor*disprovable*in second-order logic, because if it was it would also be provable or disprovable in ZFC, but it is independent of ZFC. (The sentence simply says that if there exist addition and multiplication functions, and an order relation, that make the domain into an Archimedean ordered field, then every subset of the domain is either in bijection with the entire domain or is countable. No set-theoretic axioms are mentioned in the sentence, but the sentence can be interpreted as usual as a statement within ZFC about an arbitrary set which plays the role of the domain.)

- Because you only need a finite number of axioms, in second-order logic with full semantics you can write a sentence which is satisfiable if and only if CH holds, in the signature that includes only equality. This is the sense in which full semantics decide the truth value of CH. But that sentence is neither

- OK, so I overstated the case a

- Hence, Second-order Logic is powerful enough for proving-or-refuting the Hypothesis of Continuum, yet not powerful enough for proving-or-refuting Axiom of Induction. Correct? 77.127.133.106 (talk) 00:08, 21 September 2012 (UTC)

- No, I don't think that's right. Induction is what "says" that we're talking about the natural numbers. Without induction, I don't see any reason the theory should be categorical. --Trovatore (talk) 23:30, 20 September 2012 (UTC)

- Thanks. Btw, I understand that if Second order Arithmetic - minus Axiom of Induction - is added to Second-order Logic, then Axiom of Induction will be proved-or-refuted in the new system, am I right? If I am, then I understand that - the usual reason for adding Axiom of Induction to such a complete system - is generally just for the sake of convenience, i.e just in order to have more

- Right — if it were computable, you could violate the incompleteness theorem (just take every statement implied by the theory as an axiom). --Trovatore (talk) 23:17, 20 September 2012 (UTC)

- Thank you for your quick answer (like a missile). Since you didn't refer to the first half of my second point, namely: whether Second order Arithmetic - interpreted in Second-order Logic - is not effective/computable, so I guess it's really not. All the best. 77.127.133.106 (talk) 22:12, 20 September 2012 (UTC)

- Regarding "second-order arithmetic", some care is needed. First, "second-order arithmetic" is usually considered as a
*first*order theory. But even if we study it in second-order semantics, it is generated from the same effective set of axioms as the first-order two-sorted version (we can include the choice axioms as well, depending on taste). The inference rules for second-order logic are no stronger than those for first-order logic. Thus nothing is provable that would not already be provable if we considered second-order arithmetic as a first-order theory. The effect of using full second-order semantics is simply to eliminate from consideration many models of the first order version (for example, models in which the sets don't range over*all*sets of individuals). Changing the semantics does not allow us to prove anything within the theory that was not already provable.

- Regarding "second-order arithmetic", some care is needed. First, "second-order arithmetic" is usually considered as a

- It's true that the theory of the standard model of arithmetic is a complete theory that is not effective, but this is true even in first-order logic. The effect of changing to full second-order semantics is that we eliminate all other models of second-order arithmetic from consideration. But if we just want to talk about the set of sentences true in the standard model we can do that even if we formalize arithmetic in first-order logic. — Carl (CBM · talk) 12:00, 21 September 2012 (UTC)
- Well, now wait a minute, Carl — the rules of inference are
*much*stronger in second-order logic. The rule of inference is that anything that is logically implied may be inferred, and because there's only one model (up to isomorphism),*all*true statements of arithmetic are logically implied, and therefore may be inferred. Of course the "rule" itself is not computable. --Trovatore (talk) 17:49, 21 September 2012 (UTC)- Yes, that "rule" is not computable, and it is not a rule of inference that anyone actually uses for second-order logic. In practice the rules that are used for second-order logic could also be used for first-order multi-sorted logic (and they are all verified by ZFC), with the result that there are many logical validities under full second order semantics that are not provable. The only difference between second-order logic as it is studied in the literature and first-order logic is in the semantics; the theories are syntactically interchangeable, including their deductive systems. — Carl (CBM · talk) 19:06, 21 September 2012 (UTC)
- I don't know what you mean by "actually using" second-order logic. Anyway, for the benefit of our anonymous interlocutor, let me specify that by "provable" in second-order logic, what I mean is "logically implied" in second-order logic. I don't know what else anyone
*could*mean. --Trovatore (talk) 19:22, 21 September 2012 (UTC)- A logic, after all, has a syntax and a semantics. Any reference on second-order logic is going to describe the deductive system that is normally used for it - e.g. section 3.2 of Shapiro's book. This consists of a usual deductive system for first-order logic in two sorts, something to correspond to the comprehension scheme, so that definable sets can be proven to exist, and often a system of principles analogous to the axiom of choice (Shapiro does include these, but Simpson does not, each having good reasons for their choice). In the literature, when someone talks about provability in second order logic they mean provability in a deductive system such as this. — Carl (CBM · talk) 19:51, 21 September 2012 (UTC)
- Alright, fine. I don't want to mislead anyone through my possibly idiosyncratic use of terminology here.
**Restrahnt**, please interpret my remarks as saying that second-order arithmetic as interpreted in second-order logic gives the complete theory in the sense of logical implication, rather than proof. And just a tiny bit of set theory, using second order logic, either logically implies or, what, "logically refutes" I guess? the continuum hypothesis. --Trovatore (talk) 20:09, 21 September 2012 (UTC)

- Alright, fine. I don't want to mislead anyone through my possibly idiosyncratic use of terminology here.

- A logic, after all, has a syntax and a semantics. Any reference on second-order logic is going to describe the deductive system that is normally used for it - e.g. section 3.2 of Shapiro's book. This consists of a usual deductive system for first-order logic in two sorts, something to correspond to the comprehension scheme, so that definable sets can be proven to exist, and often a system of principles analogous to the axiom of choice (Shapiro does include these, but Simpson does not, each having good reasons for their choice). In the literature, when someone talks about provability in second order logic they mean provability in a deductive system such as this. — Carl (CBM · talk) 19:51, 21 September 2012 (UTC)

- I don't know what you mean by "actually using" second-order logic. Anyway, for the benefit of our anonymous interlocutor, let me specify that by "provable" in second-order logic, what I mean is "logically implied" in second-order logic. I don't know what else anyone

- Yes, that "rule" is not computable, and it is not a rule of inference that anyone actually uses for second-order logic. In practice the rules that are used for second-order logic could also be used for first-order multi-sorted logic (and they are all verified by ZFC), with the result that there are many logical validities under full second order semantics that are not provable. The only difference between second-order logic as it is studied in the literature and first-order logic is in the semantics; the theories are syntactically interchangeable, including their deductive systems. — Carl (CBM · talk) 19:06, 21 September 2012 (UTC)

- Well, now wait a minute, Carl — the rules of inference are
- You state that: "
*It's true that the theory of the standard model of arithmetic is a complete theory that is not effective, but this is true even in first-order logic*". However, Trovatore has already presented a counter example, e.g. the proposition: "ZFC is consistent", or more formally: "*For every natural number n, n is not the Goedel number of a proof of 0=1 from the axioms of ZFC*". This proposition is neither provable nor disprovable in Second order Arithmetic (when considered as a first order theory), as Trovatore has already proved, hasn't he? 77.127.133.106 (talk) 14:42, 21 September 2012 (UTC)- The theory of the standard model of arithmetic (that is, true arithmetic but in the language of second-order arithmetic) has nothing at all to do with provability. In particular it does include the sentence Con(ZFC) because (1) the "numbers" in the standard model are the actual, standard natural numbers and (2) ZFC is consistent. — Carl (CBM · talk) 15:38, 21 September 2012 (UTC)

- It's true that the theory of the standard model of arithmetic is a complete theory that is not effective, but this is true even in first-order logic. The effect of changing to full second-order semantics is that we eliminate all other models of second-order arithmetic from consideration. But if we just want to talk about the set of sentences true in the standard model we can do that even if we formalize arithmetic in first-order logic. — Carl (CBM · talk) 12:00, 21 September 2012 (UTC)

## Monty Hall problem RFC

Hi! Over at Talk:Monty Hall problem#Conditional or Simple solutions for the Monty Hall problem? I assigned **Abstain** to your comments. If this is incorrect, please indicate "Proposal #1", "Proposal #2", or "Neither". Thanks! --Guy Macon (talk) 20:42, 20 September 2012 (UTC)

## The infinite

Hi, I was intrigued by your post on the ref desk: "worst mistake...Aristotelian rejection of the completed infinite, in favor of the potential infinite." I've found this [1], but I'm not exactly sure how you're interpreting this sort of thing. Care to share your thoughts? SemanticMantis (talk) 00:41, 23 September 2012 (UTC)

## The Unanswered Question

Greetings, Trovatore.

Always good to find someone who takes the detail of language seriously, even if we don't always agree on, er, the detail.

Which reminds me: You seem to have missed my question here. Or was your post some sort of humour that went over my head?

Cheers. -- Jack of Oz ^{[Talk]} 21:54, 8 October 2012 (UTC)

- It was just a typo. I didn't see any point in belaboring it. --Trovatore (talk) 22:24, 8 October 2012 (UTC)
- Fare enuf. -- Jack of Oz
^{[Talk]}00:23, 9 October 2012 (UTC)

- Fare enuf. -- Jack of Oz

## Other varieties of English

Re your comment on the spelling variations proposal at WP:VP/T, "just a few in some other varieties, usually barely distinguishable from British English, except for Canadian which is a mix", I had to laugh — I write some articles about Liberian topics, and it's downright tricky to write in Liberian English. Working here, I see tons of Liberian newspapers, and they seem basically to be a mix of US and British usage with tons of acronyms and occasional odd phrases (e.g. "I hold your foot" = "I beg you") thrown in. Nyttend (talk) 20:47, 6 November 2012 (UTC)

- I don't think Liberian English is a recognized variety for ENGVAR purposes. The WP:TIES section applies only to English-speaking countries. --Trovatore (talk) 20:50, 6 November 2012 (UTC)
- ? Virtually everyone either speaks English or doesn't speak a Western language; English is the only official language, and it's dominant in business and print culture. Nyttend (talk) 21:01, 6 November 2012 (UTC)

## I modified my comment after you made yours re "Third realm"

Since it was the opener for discussion, I modified my comment after you made yours re "Third realm", before others started commenting based on ambiguities in my opening comment. I am letting you know in case you might want to similarly modify yours before others start commenting. ParkSehJik (talk) 15:34, 26 November 2012 (UTC)

## Cardinal numbers

Thanks for tidying up my edit on cardinal numbers. — Preceding unsigned comment added by Jason.grossman (talk • contribs) 01:43, 27 November 2012 (UTC)

## I was wondering if this is legit

Please stop using talk pages such as Talk:Democracy for general discussion of the topic. They are for discussion related to improving the article; not for use as a forum or chat room. If you have specific questions about certain topics, consider visiting our reference desk and asking them there instead of on article talk pages. See here for more information. Thank you. Saddhiyama (talk) 10:27, 13 December 2012 (UTC)

**Am I not allowed to write things that I think contribute to a specific page... (or is it that reference crap again, even though I linked something..)**

**I just felt it was so strange that it got deleted in a small talk, was wondering what you thought... or whoever**
It is on the democracy page (TALK)** — Preceding unsigned comment added by Wickid123 (talk • contribs) 10:44, 13 December 2012 (UTC) **

## Absolutely abnormal number

In this edit you told another editor *don't use Wikipedia to make up new jargon*. If you look at the next two words after the phrase in question, you will see a reference Martin 2001 to a paper "Absolutely abnormal numbers" in the American Mathematical Monthly. Irrespective of the merits of the precise wording of the edit, it is clear that User:Nmondal was not making things up here. Deltahedron (talk) 21:08, 19 December 2012 (UTC)

## Talkback

Template:Talkback Paris1127 (talk) 22:46, 2 January 2013 (UTC)

## Spacing in contractions, esp Italian

Hi Trovatore-- Re your watching Kwami's talkpage, I wonder if I might ask you another question, that I had posted at the Village Pump, but haven't yet received a response:

- It seems clear that you never space following the apostrophe where the contracted word is an article, such as with L'elisir d'amore, or in other situations where a word might be frequently contracted, such as, just for example, "Dov'è Angelotti?" or "Mario, consenti ch'io parli?". But then you sometimes get things that it's impossible to tell from the typography, but they look strange when they're
*not*spaced, such as "Ho una casa nell' Honan" or "Nient' altro che denaro", "Quando me 'n vo soletta", "Sa dirmi, scusi, qual' è l'osteria?" etc. Are there rules for this?

In the meantime it looks as though I'm putting at least a few spaces in that latter series that ought not to be there. Milkunderwood (talk) 06:49, 8 February 2013 (UTC)

~~I also posted another question at Kwami's page, about "e shown in 'med', as opposed to 'mɛd'". He didn't know the answer, was just correcting the IPA.~~*Fixed to 'ɛ'.*Milkunderwood (talk) 06:59, 8 February 2013 (UTC)- Sorry, I don't think I can help you here. I don't know that I've ever used a space in this sort of situation. I have seen it, but not frequently enough to figure out any rules. --Trovatore (talk) 08:53, 8 February 2013 (UTC)
- Well, I guess that does pretty much answer my question - that in general there should be no spacings at all. So that is a very helpful reply. Thank you. Milkunderwood (talk) 16:47, 8 February 2013 (UTC)

- Sorry, I don't think I can help you here. I don't know that I've ever used a space in this sort of situation. I have seen it, but not frequently enough to figure out any rules. --Trovatore (talk) 08:53, 8 February 2013 (UTC)

## Talkback

Template:Talkback Jason Quinn (talk) 22:39, 12 February 2013 (UTC)

## Wikipedia:Reference_desk/Archives/Mathematics/2012_November_20#Guide_to_pronouncing_.28saying.29_mathematics_in_German

Hi, I was 96.46 in that conversation. Is what you wrote more than just a hunch on your part? It's hard to see why the French would render an English *k* by an *sh* sound, or what English really has ~~anything to~~ to do with things here.

But if they read Čech, which has that very diacritical mark, according to their own orthographic system but with allowance for the proper pronunciation of the first letter, the result would be precisely *tchèche*. 64.140.122.50 (talk) 05:05, 15 February 2013 (UTC)

- Oh, I forgot that French would pronounce the
*che*with a soft ch sound. I was thinking it would be a /k/. --Trovatore (talk) 05:14, 15 February 2013 (UTC)- All right. Thanks for clearing that up. 64.140.122.50 (talk) 06:03, 15 February 2013 (UTC)

## Am I confused as to what Harvard citations are?

I was pointed to Special:WhatLinksHere/Template:Harvard citation for examples of articles using Harvard citations and I have yet to find an example there that uses parenthetical citations rather than footnotes. Am I incorrect that Harvard citations are parenthetical citations? **Ryan*** Vesey* 04:42, 18 February 2013 (UTC)

- It appears that the template is used in some articles that don't have what I think of as Harvard cites. I'm a little confused on this point as well. One that does have parenthetical cites is Cauchy–Riemann equations. --Trovatore (talk) 04:47, 18 February 2013 (UTC)

## Your revision today

I wish you had discussed this on the talk page first. Would you care to explain, on the talk page, what you mean here?:-

*Undid revision 549743025 by Damorbel (talk) no, temperature is not kinetic energy. See Kittel & Kromer for the best accessible explanation of what temperature is.*

--Damorbel (talk) 20:45, 11 April 2013 (UTC)

- For one thing, the units of temperature and kinetic energy are not even the same.
- Also a higher temperature not only makes particles move faster and thus have more kinetic energy, it also breaks bonds, change phases, and can create particle pairs (at sufficiently high temperatures). JRSpriggs (talk) 07:09, 12 April 2013 (UTC)

## Thank You From a Necromancer

In January you gave me a really insightful and helpful response on the ref desk about Ehrenfeucht–Fraïssé games, my coming on here is fairly spotty and I didn't have a chance to reply when I first read it, so I ended up not without intending to. At any rate, though you've probably forgot what I'm even referring to at this point: Thank You:-) I love reading your contributions, a lot of your mathematical interests are the same as mine and you always seem to provide a breath of fresh insight.Phoenixia1177 (talk) 05:59, 19 April 2013 (UTC)

- Thanks much! I had a lot of fun answering that question for its own sake, but it's nice to be appreciated too. --Trovatore (talk) 07:05, 19 April 2013 (UTC)

## File:MixedFontBadness.png missing description details

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## Talkback

Template:Talkback ChrisGualtieri (talk) 20:11, 10 May 2013 (UTC)

## Redirects

Obviously, I disagree with all of the arguments for redirects, but as I am currently out numbered three to two, it is pointless to pursue the issue. Basically it is a non-issue anyway, like arguing over whether it is better to say this or that in a sentence. Both work and allow readers to get to the article in the link, and neither get there appreciably quicker. Apteva (talk) 03:33, 16 May 2013 (UTC)

## Invitation to take a short survey about communication and efficiency of WikiProjects for my research

Hi Trovatore, I'm working on a project to study the running of WikiProject and possible performance measures for it. I learn from WikiProject Mathematics talk page that you are an active member of the project. I would like to invite you to take a short survey for my study. If you are available to take our survey, could you please reply an email to me? I'm new to Wikipedia, I can't send too many emails to other editors due to anti-spam measure. Thank you very much for your time. Xiangju (talk) 15:42, 22 May 2013 (UTC)

## Misclick

Thanks for reverting me just now. It was, as you guessed, a misclick. I'll take the reference desk pages off my watchlist as I now realise that they are not for me. Warden (talk) 09:41, 12 June 2013 (UTC)

## Neutron star, black holes on ref desk

You're right, he did answer my question, but i didnt realize.Rich (talk) 09:44, 23 June 2013 (UTC)

## Its'

I mention it, and it magically appears. Weird, that. Medeis wasn't the user I was thinking of, but she still goes on to my List of Naughty Persons. -- Jack of Oz ^{[pleasantries]} 23:18, 5 August 2013 (UTC)

## Individualism, recent edits.

Hi Trovatore, thanks for your helpful comments on this. My point was though that if you saw non-compliant changes, the duty should be on you to make the required changes, while respecting the good changes which were made by Hendrick 99, (and mine afterwards).

Just to delete both edits is a backward step. Why not change the words you think need changed (I don't speak American English!), and a gentle reminder to Hendrick 99 about his non-compliance? He wasn't just being non-compliant, in my view his edit contained some very worthwhile rephrasing independently of the language issues.

TonyClarke (talk) 19:08, 8 August 2013 (UTC)

- Tony, if you examine the edit, the entire point of it was to change the English variety. This is especially clear if you examine other edits he made at about the same time. Any "good" changes that might have been included are beside the point — the entire edit should be reverted, and if you think he actually made any improvements (which is not clear to me), then those can be added separately. What good changes? --Trovatore (talk) 19:13, 8 August 2013 (UTC)
- I would add that, by my lights, there is at least a small preference for stability in articles, so that edits need to justify themselves by actively
*improving*the article. Any edit that neither helps nor harms an article, should be reverted; only edits that actually improve it deserve to stay. When a large number of changes are made in a single edit to widely varying parts of the article, if the edit has a controversial part, then the whole edit should be reverted and the changes discussed one-by-one. It is usually best to edit one piece at a time, so that it's clear what you're doing. --Trovatore (talk) 19:29, 8 August 2013 (UTC)

Hi Trovatore (a fellow biker I see!)

These are some of the changes from the beginning of the edit which I think improve the article in terms of simpler language and shorter words. The non-compliance is unfortunate, and a charitable approach would be that he/she used their own language, inadvertently non complying. Wonder if anyone has raised this with Hendrick 99?

I think there is clear evidence of an intention to improve the article, but no evidence in this edit at least of the intention to de-Americanise (or de-Americanize). Also I think we should be assessing edits on their own merits, not on the merits of previous work by the editor, unless that editor has been highlighted as persistently subversive or a vandal.

Your other point that edits should usually be made piecemeal: I don't think this should be a rule, as I have sometimes taken a whole article and rewritten it , then posted it, with no objections arising. Also I have sometimes revised a whole article or section for plain language, which can span the whole article and done piecemeal would be too burdensome. I think that is what Hendrick 99 was doing here.

So I think the article was improved, and the non-compliant parts are easily fixed. Since you raised the non-compliance, I feel you are best placed to sort it.

achieve precedence over -> supersede (simpler ) promote-> encourage (No noncompliance, also more accurate.) interests -> affairs (simpler, shorter word) makes the individual its focus -> centres around the individual (Less words, but non compliant so that not its main intent?) lend credence to -> favour, (shorter, non compliance but not its intent? would argue -> claims (shorter, better) precisely -> that it. (Shorter words)

I could go on!

In good faith

TonyClarke (talk) 11:24, 9 August 2013 (UTC)

- I don't think you're looking at the whole picture of Hendrick 99's edits. It strains credulity to claim he/she was acting in good faith. Look at the diff I posted on talk:rights and how it breaks down — every change is either from an American spelling to a Commonwealth spelling, from a neutral word to a Commonwealth spelling, or from an American spelling to a neutral word. I broke them down one by one till I got tired of it, and there weren't any exceptions in the first five or six changes.
- In this article he's been slightly cleverer, sticking in more irrelevant changes around them, but the agenda is still there. Here are some of the changes I think were the
*point*of the edit:- "emphasizes" -> "stresses" : Not particularly either better or worse as a word choice, but it takes out an "ize" spelling, which I think was why he did it.
- "makes the individual its focus" -> "centres around the individual": This one is absolutely a
*poorer*word choice; the original is clearly better. There's no reason to do it except to get in the Commonwealth spelling of "centre" - "the individualist does not lend credence to" -> "the individualist does not favour": Change in meaning here. Both the original and the new can be criticized. But the point is to add the "favour" spelling.
- "are based upon predominantly" -> "centre primarily around": Who says "centre around"? Again, that's a poorer word choice than the original.

- So basically I think there's a clear agenda here and don't buy that he's acting in good faith. However, assuming arguendo that he were, there would still be enough questionable choices to revert. I agree with you that sometimes you can do a big noncontroversial cleanup edit, but then if anyone objects to any part of it, you should expect the whole thing to be reverted. You can't make a dozen different changes in the same edit and ask people to work from
*there*, if they don't like parts of it — the whole thing gets reverted, and you discuss the changes from the status quo ante. --Trovatore (talk) 15:27, 9 August 2013 (UTC)

Not the way Jonesey95 saw one of the edits (see Hendrick 99 talk page, 4 August 2013 (UTC)), Jonesey was happy to change the bits which seemed wrong, while leaving what seemed good. Hendrick seems to me someone who is new and struggling on WIkipedia. To say this is a campaign to delete American wording is verging on paranoia: none of the other editors have seen his work this way.

To revert rather than amend is not helping someone who is struggling and perhaps a bit opinionated like most of us. It also doesn't help me, whose edit was caught up in your reversion. I don't think its fair that you are now expecting others, possibly me, to re insert the best bits of Hendrick 99's post, and also to reinsert the subsequent posts. But if you insist on maintaining your position, then so be it. Good luck. Happy cycling!

TonyClarke (talk) 17:45, 9 August 2013 (UTC)

## advice

I've undone your comments to our newest troll, [2] restoring the hat you should not have opened. If you want to give personal advice he has a talk page. Please don't put it on the ref desk. μηδείς (talk) 02:22, 9 August 2013 (UTC)

- Medeis, your hatting is frankly way out of line. I will undo it whenever I think it is appropriate. --Trovatore (talk) 02:28, 9 August 2013 (UTC)

## Not a math journal

Hi, I started the following(*) in Talk:Saturated model. I have to agree with you about your note reverting me, "relevance is unclear". I'm used to a "saturated model" being one for which no more components can be added, given the limitations of the data. A saturated experimental design produces such a dataset, given a model form. A supersaturated experimental design produces a dataset insufficient to estimate all components of a given model, relegating the experimenter to a subset model of the original one. Is there a place here for that?

(*)WP can't be a math journal. There must be a common language introduction and explanation, with no special meanings for common words used. A more technical section with special meanings can follow, but without the others leading in before, it's not encyclopedic.

This is also my reason for putting the "Technical" template back into Type (model theory). Attleboro (talk) 17:57, 15 August 2013 (UTC)

- Hi Attleboro,
- You're right that WP is not a math journal. However it does not follow that all articles will be accessible to all readers, or will even have any
*part*that is accessible to all readers. There is no upper limit at all to how*difficult*a topic can be, and still be appropriate for WP. - The appropriate criterion is, whether the material is as understandable as it reasonably
*can*be, given the inherent difficulty of the subject matter. - I don't even necessarily
*disagree*with you about the section you flagged in type (model theory). But you don't get to just plop the {{technical}} tag down there and leave, just because you personally don't get anything out of it. How do we know you have the background even to*know*whether it's written overly technically, given the subject matter? --Trovatore (talk) 18:34, 15 August 2013 (UTC)

Oh, as to the question about saturated models: There's a hatnote at the top of the saturated model article, directing you to the article on structural equation modeling, which may be what you're looking for. If that meaning is one that a lot of people are looking for, then it's possible that saturated model ought to be a disambig page. I'm not opposed to that if it's justified; please bring it up on the talk page. --Trovatore (talk) 18:37, 15 August 2013 (UTC)

- Thanks for pointing out that note. I have a sneaking suspicion there may be a way to get from the formal definition in the article to the more common usage, or vice versa, but it's beyond me at the moment. I really disagree about
of some articles being accessible to all readers. Otherwise, why separate WP by languages? Without a common language introductory section, the Tower of Babel looms over us all. Attleboro (talk) 20:20, 15 August 2013 (UTC)**no part**- If there's a connection between the model-theory usage and the statistics usage, it's completely obscure to me. But then I don't know anything about the stats usage, so I can't prove it either way. But if there is, I expect it's almost by coincidence; I don't think there are a lot of workers who do both model theory and statistics, so most likely the usages developed independently and in ignorance of each other.
- We
*are*using the same language, English. No one knows all of English, though. --Trovatore (talk) 20:43, 15 August 2013 (UTC)

## Ice Hockey

My mistake. I saw that the IP editor was changing the English styles and assumed they were changing them from the established usage.--Asher196 (talk) 03:22, 30 August 2013 (UTC)

## Godel

I don't see why there should be a top level religion section. Check out the other articles on people. Very few of them have religion sections at all and those that due have more filled out about other parts of the persons life. Should every article about a person have a religion section? Or is there something particularly important involving Kurt Gödel and religion that makes it worth mentioning? I don't think either is the case but maybe I am missing something. To me it is not more worthy of having its own section than say Godel's political views or something. Lonjers (talk) 02:35, 28 September 2013 (UTC)

Blah, I guess to be clear I am not disputing this based on a lack of information but based on notoriety/importance. Lonjers (talk) 02:40, 28 September 2013 (UTC)

- Well, this is not something where there's going to be an absolute answer, but my feeling is that this material is more important for Goedel than it would be for a lot of other math/philosophy folks. Among latter-20th-century analytic philosophers, Goedel was one of the very few (at least, not coming from the perspective of a specific revealed-theological system) who openly challenged materialism and was willing to say he though the ego survives death. --Trovatore (talk) 20:10, 28 September 2013 (UTC)

## Ron Paul

The piped link I supplied goes to a *particular section* of the article. This is because I did a WP:BLAR on the Peace & Prosperity article. Please let me know here what you think. – S. Rich (talk) 04:55, 30 September 2013 (UTC)

- I fixed the redirect so that it goes to that section. If the Peace & Prosperity article is someday revived, the redirect will automatically go to the right place, but the pipe would not. --Trovatore (talk) 04:58, 30 September 2013 (UTC)

Template:Ec Oh! I see what you've done on the redirect article. So is there a need to redo the other "what links here" articles? Thanks. – S. Rich (talk) 04:59, 30 September 2013 (UTC)

## UPDATING AN AGED PICTURE

Hi Mike !

I was wondering if you can help me to update an aged picture for this guy "Salvatore Cuffaro". The picture currently on display is very old (2006) and the guy has also drastically changed in appearance becoming remarkably thinner. He was a former italian politician now jailed.

Here are 2 more recent images one is in b/w .. the other in colour .. as you can see the looks very different from the pic that is actually on display

http://www.sciclinews.com/immagini_articoli/1355416600_cuffaro_dimagrito.jpg

http://www.pellerito.it/wp-content/uploads/2013/10/cuffaro.jpg

Thanks very much for your help.

- ) — Preceding unsigned comment added by 88.112.193.20 (talk) 08:57, 25 October 2013 (UTC)

He is this one :

http://en.wikipedia.org/wiki/Salvatore_Cuffaro — Preceding unsigned comment added by 88.112.193.20 (talk) 00:29, 26 October 2013 (UTC)

- Well, OK, I was being slightly euphemistic. I suppose I
*could*help if I really wanted to — I could go digging around and see if anyone has a recent PD photo of him (unlikely but you never know). But why me, given that I never heard of him? Surely you're just as qualified to do it as I am (maybe more so, since you know something about hime to start with)? --Trovatore (talk) 00:43, 26 October 2013 (UTC)

- Well, OK, I was being slightly euphemistic. I suppose I

## Andy

Can you maybe comment on Andy's page. I generally find his hattings helpful, but this just seems overboard. I don't want to have to take this to uw3rr. μηδείς (talk) 04:36, 20 November 2013 (UTC)

## Compact space

I agree with your edit; I wanted to link it as point-set topology (which was recently split from general topology), but I thought people wouldn't know what it is. Should I link to it anyways? General topology is no longer a helpful link for basics in topology, so I would liketo change it to something, but I would appreciate your feedback.Brirush (talk) 02:55, 30 November 2013 (UTC)

- I think your new work at point-set topology looks good, but I would like to see it at general topology instead. I don't think the subjects are different enough for two articles. I've started a discussion at talk:general topology; comment invited there. --Trovatore (talk) 03:00, 30 November 2013 (UTC)

## topoligical

I doubt "topoligical" exists in any English variant. Please be more careful before reverting, it is extremely annoying to have good faith edits reverted blindly. As to "neighbourhood" / "neighborhood" I have never before seen the "neighborhood" variant (I am Portuguese), and so I understand the correction, but it would be appreciate that a good faith edit would deserve more than blunt revert with some automated summary. - Nabla (talk) 00:47, 6 December 2013 (UTC)

- I restored the good spelling correction. I deliberately did two edits, one as an undo to point out the ENGVAR issue (it wasn't just an automated summary; I explained), followed by a second one to restore your fix to "topoligical". --Trovatore (talk) 00:56, 6 December 2013 (UTC)
- You reverted the good spelling correction. - Nabla (talk) 01:52, 6 December 2013 (UTC)
- In the
*first*edit. Then I immediately put it back. As I explained, this was on purpose. --Trovatore (talk) 02:10, 6 December 2013 (UTC)- You reverted a good faith edit, and a good edit, for no good reason, except imposing some English variant, on purpose. Exactly how does that help? - Nabla (talk) 10:45, 14 December 2013 (UTC)
- He did not "revert" an edit- that would have led to an edit summary that begins with the word "Reverted". He
*undid*an edit, and appropriately, because it was not appropriate to change "neighborhood" to "neighbourhood". It would also be inappropriate to change "neighbourhood" to "neighborhood" in an article that uses British spelling. Then he re-did the useful part of the edit to fix the spelling of "topological". I don't see any issue. — Carl (CBM · talk) 15:37, 14 December 2013 (UTC)

- He did not "revert" an edit- that would have led to an edit summary that begins with the word "Reverted". He

- You reverted a good faith edit, and a good edit, for no good reason, except imposing some English variant, on purpose. Exactly how does that help? - Nabla (talk) 10:45, 14 December 2013 (UTC)

- In the

- You reverted the good spelling correction. - Nabla (talk) 01:52, 6 December 2013 (UTC)

## Removal of the trajectory section in Exponentiation

Trovatore, that is ridiculous. Have you indeed just removed the x^{y} curvature trajectory section there, which also contained reputable sources about such trajectories (and also a text, not only the illustrating pic!), because this section would teach in your opinion the topic not anymore *tranquilly* and *gently* enough?

All mathematical topics which are not content in any known *teaching plans of schools* should kept away from all encyclopedias?? --MathLine (talk) 23:46, 7 December 2013 (UTC)

- We're not supposed to
*teach*at all. Wikipedia is a reference work, not a textbook. The question is, is that section something that one would normally expect to find in a reference work on exponentiation in general? - My opinion is, it is not. But certainly the matter is open for discussion. Feel free to open a section on the talk page. --Trovatore (talk) 02:20, 8 December 2013 (UTC)

## Confusing leads in field hockey articles.

2013 Men's Hockey Junior World Cup is an article with out field hockey being distinguished in the lead. To me its confusing, but i am unable to do anything. Can someone take a look at it. — Preceding unsigned comment added by 76.64.228.14 (talk) 00:58, 17 December 2013 (UTC)

- I don't see a real problem here. The first link is to Hockey Junior World Cup, and the first link there is to field hockey, unpiped, so that the reader sees "field hockey" in the text. The 2013 Men's Hockey Junior World Cup article is in near-stub state; if it's expanded to talk about "hockey", as opposed to proper names that contain "hockey", then yes, it should say "field hockey" at first reference.
- I'm not quite sure what you mean you're "unable to do anything" -- the article is not semi-protected; you can edit it if you want to. --Trovatore (talk) 07:21, 17 December 2013 (UTC)

## Infinity

Hi Trovatore, while I generally support and respect your edits and opinions, I can not see how you could justify the statements about infinity that I removed and you reverted to. I'm sure that this has been discussed somewhere and you might point me to that, but I have spent too many years disabusing students of such notions to be easily convinced that I am wrong about this. I do not wish to be involved in any edit wars, but I do feel strongly about this, and would like to hear your rationale before I remove the offending remarks as being unsourced. Bill Cherowitzo (talk) 18:37, 19 December 2013 (UTC)

- Sorry, I have a bit of a chip on my shoulder about the meaningless "infinity is not a number" assertion; neither "infinity" nor "number" is well enough specified to be able to recover any information from that cliché. There are certainly things called "infinity" in some contexts, that are also called "numbers" in some contexts. The language you removed seemed to me to be talking primarily about the infinity of the extended reals. --Trovatore (talk) 19:47, 19 December 2013 (UTC)

Interesting, but here are a couple of random thoughts. I don't see how the even more vague "...often treated as if it were a number" can have any more meaning than the cliché. While I have found the cliché to be pedagogically useful at times, I do agree that it is not well enough specified to be considered as a meta-theorem. When infinity is used in the context of the extended reals or any one-point compactification, it is the symbol and not the concept which is being used. If it takes on any numerical aspects, it is because it is defined to have them, they are not intrinsic. The only property that is implied by the use of this symbol, and the one that makes this a natural choice, is its lack of membership in the set being extended. Note that I am not arguing against the existence of infinite numerical things (hyperreals, infinite cardinals or ordinals, etc.). These things have numerical qualities because of their definitions, not because of their trans-finite nature. Also, the projective geometer's "points and lines at infinity" have no numerical connotation at all, so "often" would have to exclude geometric and topological uses. Not surprisingly, I find the sentence I removed as both inaccurate and misleading and I think we are doing a dis-service to the readers who come to this page looking for clarification of their own confused views of infinity. I'll put my thoughts on how I'd like to fix the article on its talk page. Bill Cherowitzo (talk) 18:52, 20 December 2013 (UTC)

- Hmm, no, I don't really agree with your take on the extended reals. It's not just a symbol. It's an (extended) "number" bigger than any finite number. That's conceptually infinity. --Trovatore (talk) 19:23, 20 December 2013 (UTC)

Please indulge me for just a little longer. I am not trying to argue for my POV but rather attempting to clarify my thinking, and that is easier to do in dialogue (at least for me). In your response you talk about the (extended) "number", an infinite object, and I am perfectly ok with that (I'd prefer to call it a transfinite number, but that is just a minor point). Then you say that it is conceptually infinity and all sorts of red flags go up in my mind. It seems that I am reluctant to use the term "infinity" in reference to an object. Yet, when talking about elliptic curves, the point at infinity is routinely denoted by ∞ and is called "infinity" and I am perfectly happy with that! The two situations appear to be analogous so I am looking for an explanation (other than the possibility that I am schizophrenic ;^)) of why I see them differently. I think that in the elliptic curve case I can accept that usage because it is totally formalistic and symbolic–there is nothing intrinsically special about the point in question, its special role is an accident of the choice of coordinates. In order to make the extended reals work for me, without the red flags, I need to transfer this formalistic view to them, which is what I meant when I said that infinity was just being used as a symbol. So, does any of this make sense or am I creating a mountain out of a mole hill? Are there any implications here for how to organize the infinity article? Bill Cherowitzo (talk) 19:17, 21 December 2013 (UTC)

- Before you start reorganizing the article Infinity, you should read the article Finite set and realize that infinite sets are the norm and finite sets are the special case. JRSpriggs (talk) 03:15, 22 December 2013 (UTC)

- Hi Bill, OK, maybe this will clarify how I see things a bit.
- I remember listening to a baseball announcer talking about a pitcher who had recently been called up to the majors. He had an earned run charged to him, but he had not yet gotten anybody out.
- The announcer said, "The next time this guy gets an out, his ERA will go down (from what it is now). Because it
*is*infinity." - Was he wrong? I don't think he was wrong. He was implicitly working in the structure [0,∞] (or, well, the corresponding thing on the rationals, if you want to get picky). The pitcher's ERA was something over 0, which was ∞. That was a worse ERA than it was possible to have if you had ever gotten anybody out, so it was correctly called ∞. To me this is not a formalistic trick; I'd call it the reality, correctly understood.
- I don't know whether you buy this or not, but hopefully it makes it clearer how I'm looking at it. --Trovatore (talk) 21:00, 22 December 2013 (UTC)

## Inaccessible cardinal

Hey, I saw your revert. Why not just correct the text. The letters should still be defined before they're used, not after. The bits of that article are out of order. Crasshopper (talk) 21:58, 19 January 2014 (UTC)

- On reviewing the passage in question, I do kind of think you have a point. Unfortunately the text is in worse shape than I realized and it's not a trivial fix. I really just looked at the diff of your edit and thought it wasn't really in the right direction, which I still think, but I'm not sure what the best solution is. --Trovatore (talk) 06:46, 20 January 2014 (UTC)

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## Borel σ-algebra

Continuing our discussion on that article ... Yeah, it didn't occur to me to use the axiom of choice, but I get your explanation. I'd like to hear more about the representation you mention (for my own curiosity). I'm guessing it depends on the axiom of choice too, as well as other high-level set theory. It would be a stretch even to say I'm a novice in modern set theory, but I do have some acquaintance with it. Maybe you can give me the gist in terms that are more analytic or topological? Daren Cline 01:48, 5 March 2014 (UTC) — Preceding unsigned comment added by Darencline (talk • contribs)