Modal logic - Revision history

24.23.138.165: /* Axiomatic systems */

2015-01-01T00:05:19Z

Axiomatic systems

← Older revision		Revision as of 02:05, 1 January 2015
Line 1:		Line 1:
	~~It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-~~the~~-counter pain medication~~ is ~~just masking the problem~~. ~~Seeing an emergency dentist~~ is ~~critical to getting the source of the problem diagnosed and corrected as soon as possible.<br><br>Here are some common dental emergencies~~:~~<br>Toothache: The most common dental emergency~~. ~~This generally means a badly decayed tooth. As the pain affects the tooth~~'s ~~nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched~~. ~~Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves~~ and ~~insert it in the cavity. This will give temporary relief until a dentist can be reached.<br><br>At times the pain may have a more obscure location such~~ as ~~decay under an old filling. As this can be only corrected by a dentist there are two things~~ you ~~can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet~~ in ~~a half glass (4 oz) of warm water holding~~ it ~~in the mouth~~ for ~~several minutes before spitting it out~~. ~~DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN~~.~~<br><br>Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be~~ to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.<br><br>Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.<br><br>Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.<br><br>~~Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head~~ to ~~immobilize the jaw until you can get the patient~~ to ~~a dentist or the emergency room of a hospital.<br><br>Painful Erupting Tooth~~: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of ~~the cold, along with an appropriate dose of aspirin, usually provides temporary relief.<br><br>In young adults, an erupting 3rd molar~~ (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.<br><br>If you adored this informative article and also you wish to get more info with regards to [http://~~www~~.~~youtube~~.com~~/watch?v=90z1mmiwNS8 Washington DC Dentist~~] ~~generously pay a visit to our own website.~~		Person who wrote the articles is called Eusebio. South Carolina is [http://Michaelsbirth.org/ michael's birth] place. The favourite hobby for him and as well his kids is to assist you fish and he's resulted in being doing it for quite some time. Filing has been his profession as news got around. Go to his website track down out more: http://circuspartypanama.com<br><br>

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79.93.13.35: /* External links */

2014-02-17T22:38:16Z

External links

← Older revision		Revision as of 00:38, 18 February 2014
Line 1:		Line 1:
	~~{{refimprove\|date=September 2012}}~~		It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.<br><br>Here are some common dental emergencies:<br>Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.<br><br>At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.<br><br>Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.<br><br>Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.<br><br>Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.<br><br>Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.<br><br>Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.<br><br>In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.<br><br>If you adored this informative article and also you wish to get more info with regards to [http://www.youtube.com/watch?v=90z1mmiwNS8 Washington DC Dentist] generously pay a visit to our own website.
	~~In [[mathematics]],~~ a ~~'''nowhere continuous function'''~~, ~~also called~~ an ~~'''everywhere discontinuous function'''~~, is ~~a [[function (mathematics)\|function]] that~~ is ~~not [[continuous function\|continuous]] at any point of its [[domain~~ of a ~~function\|domain]]~~. If '~~'f'' is a function from [[real number]]~~s to ~~real numbers, then ''f''(''x'') is nowhere continuous~~ if ~~for each point ''x'' there~~ is ~~an ε > 0 such that for each δ > 0 we can find~~ a ~~point ''y'' such that \|''x'' − ''y''\| < δ~~ and ~~\|''f''(''x'') − ''f''(''y'')\| ≥ ε~~. ~~Therefore, no matter how close we get to any fixed point, there are even closer points at which~~ the ~~function takes not-nearby values~~.

	~~More general definitions of~~ this ~~kind of function~~ can be ~~obtained,~~ by ~~replacing~~ the ~~[[absolute value]] by the distance function in~~ a ~~[[metric space]],~~ or ~~by using the definition of continuity~~ in a ~~[[topological space]].~~

	~~==Dirichlet function==~~
	~~One example~~ of ~~such a function is~~ the ~~[[indicator function]] of the [[rational number]]s, also known as the '''Dirichlet function''', named after German mathematician [[Peter Gustav Lejeune Dirichlet]]~~.<~~ref~~>~~Lejeune Dirichlet, P~~. G. ~~(1829) "Sur la convergence des séries trigonométriques qui servent à répresenter une fonction arbitraire entre des limites donées" [On~~ the ~~convergence~~ of ~~trigonometric series which serve to represent an arbitrary function between given limits]~~, ~~''Journal für reine und angewandte Mathematik'' [Journal for pure~~ and ~~applied mathematics (also known as ''Crelle's Journal''~~)~~], vol~~. 4, ~~pages 157 - 169~~.<~~/ref~~> ~~This function is written ''I''~~<~~sub>'''Q'''</sub~~> and ~~has [[domain~~ of ~~a function\|domain]] and [[codomain]] both equal~~ to the ~~[[real number]]s~~. ~~''I''~~<~~sub~~>~~'''Q'''~~<~~/sub~~>~~(''x'') equals 1 if ''x'' is~~ a ~~[[rational number]]~~ and ~~0 if ''x'' is not rational~~. ~~If we look at this function~~ in the ~~vicinity of some number ''y'', there are~~ two ~~cases:~~
	*If ''y'' is rational, ~~then ''f''(''y'') = 1. To show~~ the ~~function is not continuous at ''y'', we need~~ to ~~find an ε such that no matter how small we choose δ, there will be points ''z'' within δ~~ of ~~''y'' such that ''f''(''z'') is not within ε of ''f''(''y'') = 1. In fact, 1/2 is such an ε. Because the [[irrational number]]s are [[dense set\|dense]] in~~ the ~~reals, no matter what δ we choose we can always find an irrational ''z'' within δ of ''y'', and ''f''(''z'') = 0 is at least 1/2 away from 1~~.
	*If '~~'y''~~ is ~~irrational~~, ~~then ''f''(''y'') = 0~~. ~~Again~~, ~~we can take ε = 1/2, and this time~~, ~~because~~ the ~~rational numbers are dense in~~ the ~~reals, we~~ can ~~pick ''z''~~ to be a ~~rational number as close to ''y'' as is required. Again, ''f''(''z'') = 1 is more than 1/2 away from ''f''(''y'') = 0.~~
	~~In plainer terms, between any two irrationals, there is a rational, and vice versa.~~

	~~The ''Dirichlet function'' can be constructed as~~ the ~~double pointwise limit~~ of a ~~sequence of continuous functions, as follows:~~

	:<~~math~~>~~f(x)=\lim_{k\to\infty}\left(\lim_{j\to\infty}\left(\cos(k!\pi x)^{2j}\right)\right)~~<~~/math~~>

	~~for integer ''j'' and ''k''.~~

	~~This shows that the ''Dirichlet function'' is~~ a ~~[[Baire function\|Baire class]] 2 function~~. ~~It cannot~~ be a ~~Baire class 1 function because~~ a ~~Baire class 1 function can only be discontinuous~~ on ~~a [[meagre set]]~~.<~~ref~~>~~{{cite book~~
	~~\| last = Dunham~~
	~~\| first = William~~
	~~\| title = The Calculus Gallery~~
	~~\| publisher = Princeton University Press~~
	~~\| date = 2005~~
	~~\| pages = 197~~
	~~\| isbn = 0-691-09565-5 }}~~<~~/ref~~>

	In ~~general~~, if ~~''E''~~ is ~~any subset of a [[topological space]] ''X'' such that both ''E'' and the complement of ''E'' are dense in ''X''~~, ~~then~~ the ~~real-valued function which takes~~ the ~~value 1 on ''E'' and 0 on~~ the ~~complement~~ of ~~''E'' will~~ be ~~nowhere continuous. Functions~~ of this ~~type were originally investigated by [[Peter Gustav Lejeune Dirichlet]]~~.

	~~==Hyperreal characterisation==~~
	A ~~real function ''f'' is nowhere continuous if its natural [[Hyperreal number\|hyperreal]] extension has~~ the ~~property that every ''x'' is infinitely close to a ''y'' such that~~ the ~~difference ''f(x)-f(y)'' is appreciable (i.e., not [[infinitesimal]]).~~

	~~==See also==~~
	*[[Thomae%27s function]] (also known as the ~~popcorn function) — a function that is continuous~~ at ~~all irrational numbers~~ and ~~discontinuous at all rational numbers~~.

	~~==References==~~
	<~~references /~~>

	~~==External links==~~
	* {{springer\|title=Dirichlet-function\|id=p/d032860}}
	* [http://~~mathworld~~.~~wolfram~~.com/~~DirichletFunction.html Dirichlet Function — from MathWorld~~]
	* [http://demonstrations.wolfram.~~com/TheModifiedDirichletFunction/ The Modified Dirichlet Function] by George Beck, [[The Wolfram Demonstrations Project]].~~

	~~[[Category:Topology]]~~
	~~[[Category:Mathematical analysis]]~~
	~~[[Category:Types of functions]]~~

en>Mindmatrix: Reverted edits by 210.212.85.99 (talk) to last version by AugPi

2014-02-03T14:49:26Z

Reverted edits by 210.212.85.99 (talk) to last version by AugPi

← Older revision		Revision as of 16:49, 3 February 2014
Line 1:		Line 1:
	If ~~you have the desire~~ to ~~procedure settings instantaneously~~, ~~loading files quickly, nevertheless your body~~ is ~~logy plus torpid, what would~~ we ~~do? If you are~~ a ~~giant "switchboard"~~ that ~~is lack of effective management system~~ and ~~effective housekeeper~~, ~~what would~~ we ~~do? If you have send the exact commands~~ to ~~your notice~~, ~~nevertheless~~ the ~~body may~~ not ~~perform properly~~, ~~what would you do? Yes! You want~~ a ~~full~~-~~featured repair registry!~~<br><br>~~So one day my computer suddenly started being strange. I was thus frustrated, because my files were lost,~~ and ~~I cannot open~~ the ~~files which~~ I ~~required, plus then, suddenly, everything stopped working!~~<br><br>So, ~~this advanced dual scan~~ is not ~~merely among the better~~, ~~however it happens~~ to be ~~furthermore freeware. And as~~ of ~~all of this which countless regard CCleaner one~~ of the ~~greater registry cleaners inside~~ the ~~market now. I would add that I personally~~ choose ~~Regcure for the simple reason that it has a better interface~~ and ~~I learn for a truth it~~ is ~~ad-ware without charge~~.~~<br><br>First~~, ~~usually clean your PC plus keep it free of dust and dirt~~. ~~Dirt clogs up all fans~~ and ~~may cause~~ the PC to ~~overheat. We equally have~~ to ~~clean up disk area inside order to create a computer run faster~~. ~~Delete temporary plus unwanted files plus unused programs~~. ~~Empty the recycle bin~~ and ~~remove programs you~~'~~re not using.~~<br><br>~~So to fix this, we just need to be able to create all of the registry files non-corrupted again~~. This ~~may dramatically accelerate~~ the ~~loading time of your computer and allows we to do~~ a ~~big amount of items on it again~~. ~~And fixing these files couldn't~~ be ~~easier - you really require to employ~~ a ~~tool called~~ a [~~http://bestregistrycleanerfix.com/tune-up-utilities tuneup utilities~~].<br><br>~~Software errors or hardware mistakes which happen whenever running Windows plus intermittent errors are the~~ general ~~factors for~~ a ~~blue screen bodily memory dump. New software or motorists~~ that ~~have been installed or changes~~ in the ~~registry settings are~~ the ~~typical s/w causes~~. ~~Intermittent mistakes refer~~ to ~~failed program memory/ difficult disk or over heated processor and these too may cause~~ the ~~blue screen bodily memory dump error.<br><br>The System File Checker~~ (~~SFC~~) ~~could enable in resolving error 1721 because it~~, ~~by its nature, scans~~ the ~~program files for corruption~~ and ~~replaces them with their authentic versions. This requires you to have the Windows Installation DVD ROM for continuing~~.<br>~~<br>What I would suggest is to search on your for registry cleaners~~. ~~You can do this with a Google search~~. ~~Whenever you find goods, look for reports and testimonials regarding the product~~. ~~Next you can see how others like the product~~, ~~and how well it works~~.		{{refimprove\|date=September 2012}}
			In [[mathematics]], a '''nowhere continuous function''', also called an '''everywhere discontinuous function''', is a [[function (mathematics)\|function]] that is not [[continuous function\|continuous]] at any point of its [[domain of a function\|domain]]. If ''f'' is a function from [[real number]]s to real numbers, then ''f''(''x'') is nowhere continuous if for each point ''x'' there is an ε > 0 such that for each δ > 0 we can find a point ''y'' such that \|''x'' − ''y''\| < δ and \|''f''(''x'') − ''f''(''y'')\| ≥ ε. Therefore, no matter how close we get to any fixed point, there are even closer points at which the function takes not-nearby values.

			More general definitions of this kind of function can be obtained, by replacing the [[absolute value]] by the distance function in a [[metric space]], or by using the definition of continuity in a [[topological space]].

			==Dirichlet function==
			One example of such a function is the [[indicator function]] of the [[rational number]]s, also known as the '''Dirichlet function''', named after German mathematician [[Peter Gustav Lejeune Dirichlet]].<ref>Lejeune Dirichlet, P. G. (1829) "Sur la convergence des séries trigonométriques qui servent à répresenter une fonction arbitraire entre des limites donées" [On the convergence of trigonometric series which serve to represent an arbitrary function between given limits], ''Journal für reine und angewandte Mathematik'' [Journal for pure and applied mathematics (also known as ''Crelle's Journal'')], vol. 4, pages 157 - 169.</ref> This function is written ''I''<sub>'''Q'''</sub> and has [[domain of a function\|domain]] and [[codomain]] both equal to the [[real number]]s. ''I''<sub>'''Q'''</sub>(''x'') equals 1 if ''x'' is a [[rational number]] and 0 if ''x'' is not rational. If we look at this function in the vicinity of some number ''y'', there are two cases:
			*If ''y'' is rational, then ''f''(''y'') = 1. To show the function is not continuous at ''y'', we need to find an ε such that no matter how small we choose δ, there will be points ''z'' within δ of ''y'' such that ''f''(''z'') is not within ε of ''f''(''y'') = 1. In fact, 1/2 is such an ε. Because the [[irrational number]]s are [[dense set\|dense]] in the reals, no matter what δ we choose we can always find an irrational ''z'' within δ of ''y'', and ''f''(''z'') = 0 is at least 1/2 away from 1.
			*If ''y'' is irrational, then ''f''(''y'') = 0. Again, we can take ε = 1/2, and this time, because the rational numbers are dense in the reals, we can pick ''z'' to be a rational number as close to ''y'' as is required. Again, ''f''(''z'') = 1 is more than 1/2 away from ''f''(''y'') = 0.
			In plainer terms, between any two irrationals, there is a rational, and vice versa.

			The ''Dirichlet function'' can be constructed as the double pointwise limit of a sequence of continuous functions, as follows:

			:<math>f(x)=\lim_{k\to\infty}\left(\lim_{j\to\infty}\left(\cos(k!\pi x)^{2j}\right)\right)</math>

			for integer ''j'' and ''k''.

			This shows that the ''Dirichlet function'' is a [[Baire function\|Baire class]] 2 function. It cannot be a Baire class 1 function because a Baire class 1 function can only be discontinuous on a [[meagre set]].<ref>{{cite book
			\| last = Dunham
			\| first = William
			\| title = The Calculus Gallery
			\| publisher = Princeton University Press
			\| date = 2005
			\| pages = 197
			\| isbn = 0-691-09565-5 }}</ref>

			In general, if ''E'' is any subset of a [[topological space]] ''X'' such that both ''E'' and the complement of ''E'' are dense in ''X'', then the real-valued function which takes the value 1 on ''E'' and 0 on the complement of ''E'' will be nowhere continuous. Functions of this type were originally investigated by [[Peter Gustav Lejeune Dirichlet]].

			==Hyperreal characterisation==
			A real function ''f'' is nowhere continuous if its natural [[Hyperreal number\|hyperreal]] extension has the property that every ''x'' is infinitely close to a ''y'' such that the difference ''f(x)-f(y)'' is appreciable (i.e., not [[infinitesimal]]).

			==See also==
			*[[Thomae%27s function]] (also known as the popcorn function) — a function that is continuous at all irrational numbers and discontinuous at all rational numbers.

			==References==
			<references />

			==External links==
			* {{springer\|title=Dirichlet-function\|id=p/d032860}}
			* [http://mathworld.wolfram.com/DirichletFunction.html Dirichlet Function — from MathWorld]
			* [http://demonstrations.wolfram.com/TheModifiedDirichletFunction/ The Modified Dirichlet Function] by George Beck, [[The Wolfram Demonstrations Project]].

			[[Category:Topology]]
			[[Category:Mathematical analysis]]
			[[Category:Types of functions]]

en>InverseHypercube: unspacing em dash

2012-08-27T09:31:14Z

unspacing em dash

New page

If you have the desire to procedure settings instantaneously, loading files quickly, nevertheless your body is logy plus torpid, what would we do? If you are a giant "switchboard" that is lack of effective management system and effective housekeeper, what would we do? If you have send the exact commands to your notice, nevertheless the body may not perform properly, what would you do? Yes! You want a full-featured repair registry! So one day my computer suddenly started being strange. I was thus frustrated, because my files were lost, and I cannot open the files which I required, plus then, suddenly, everything stopped working! So, this advanced dual scan is not merely among the better, however it happens to be furthermore freeware. And as of all of this which countless regard CCleaner one of the greater registry cleaners inside the market now. I would add that I personally choose Regcure for the simple reason that it has a better interface and I learn for a truth it is ad-ware without charge. First, usually clean your PC plus keep it free of dust and dirt. Dirt clogs up all fans and may cause the PC to overheat. We equally have to clean up disk area inside order to create a computer run faster. Delete temporary plus unwanted files plus unused programs. Empty the recycle bin and remove programs you're not using. So to fix this, we just need to be able to create all of the registry files non-corrupted again. This may dramatically accelerate the loading time of your computer and allows we to do a big amount of items on it again. And fixing these files couldn't be easier - you really require to employ a tool called a [http://bestregistrycleanerfix.com/tune-up-utilities tuneup utilities]. Software errors or hardware mistakes which happen whenever running Windows plus intermittent errors are the general factors for a blue screen bodily memory dump. New software or motorists that have been installed or changes in the registry settings are the typical s/w causes. Intermittent mistakes refer to failed program memory/ difficult disk or over heated processor and these too may cause the blue screen bodily memory dump error. The System File Checker (SFC) could enable in resolving error 1721 because it, by its nature, scans the program files for corruption and replaces them with their authentic versions. This requires you to have the Windows Installation DVD ROM for continuing. What I would suggest is to search on your for registry cleaners. You can do this with a Google search. Whenever you find goods, look for reports and testimonials regarding the product. Next you can see how others like the product, and how well it works.