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{{Unreferenced|date=December 2009}}
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.
In [[set theory]], the '''successor''' of an [[ordinal number]] ''α'' is the smallest ordinal number greater than ''α''.  An ordinal number that is a successor is called a '''successor ordinal'''.  Every ordinal other than 0 is either a successor ordinal or a [[limit ordinal]].


Using [[von Neumann]]'s ordinal numbers (the standard model of the ordinals used in set theory), the successor ''S''(''α'') of an ordinal number ''α'' is given by the formula
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
* Only registered users will be able to execute this rendering mode.
* Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.


:<math>S(\alpha) = \alpha \cup \{\alpha\}.</math>
Registered users will be able to choose between the following three rendering modes:  


Since the ordering on the ordinal numbers α&nbsp;<&nbsp;β if and only if ''α''&nbsp;∈&nbsp;''β'', it is immediate that there is no ordinal number between α and ''S''(α), and it is also clear that α&nbsp;<&nbsp;''S''(α). 
'''MathML'''
:<math forcemathmode="mathml">E=mc^2</math>


The successor operation can be used to define [[ordinal arithmetic|ordinal addition]] rigorously via [[transfinite induction|transfinite recursion]] as follows:
<!--'''PNG'''  (currently default in production)
:<math forcemathmode="png">E=mc^2</math>


:<math>\alpha + 0 = \alpha\!</math>
'''source'''
:<math>\alpha + S(\beta) = S(\alpha + \beta)\!</math>
:<math forcemathmode="source">E=mc^2</math> -->


and for a limit ordinal λ
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].


:<math>\alpha + \lambda = \bigcup_{\beta < \lambda} (\alpha + \beta)</math>
==Demos==


In particular, ''S''(α) = α + 1. Multiplication and exponentiation are defined similarly.
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:


The successor points and zero are the [[isolated point]]s of the class of ordinal numbers, with respect to the [[order topology]].


==See also==
* accessibility:
*[[ordinal arithmetic]]
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
*[[limit ordinal]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
*[[successor cardinal]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


{{DEFAULTSORT:Successor Ordinal}}
==Test pages ==
[[Category:Ordinal numbers]]


[[cs:Izolovaný ordinál]]
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
[[de:Nachfolger (Mathematik)]]
*[[Displaystyle]]
[[fr:Ordinal successeur]]
*[[MathAxisAlignment]]
[[ko:따름서수]]
*[[Styling]]
[[pl:Następnik liczby porządkowej]]
*[[Linebreaking]]
[[sk:Izolovaný ordinál]]
*[[Unique Ids]]
[[zh:后继序数]]
*[[Help:Formula]]
 
*[[Inputtypes|Inputtypes (private Wikis only)]]
*[[Url2Image|Url2Image (private Wikis only)]]
==Bug reporting==
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .

Latest revision as of 23:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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