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Page title matches

• Axiom of completeness/Statement
  304 B (43 words) - 13:57, 2 June 2016
• Axiom of completeness
  ...al numbers, although first years are often ''given'' it as if it were an [[axiom]]; it may be proved if one constructs [[the real numbers]] "properly"}} ==[[Axiom of completeness/Statement|Statement]]==
  467 B (69 words) - 13:06, 30 July 2016
• Axiom schema of replacement
  The ''axiom schema of replacement'' posits that if {{M|F}} is some [[class function]] t
  2 KB (390 words) - 15:28, 5 April 2017
• Replacement axiom
  #REDIRECT [[Axiom schema of replacement]]
  67 B (8 words) - 23:18, 8 March 2017
• Axiom of regularity
  #REDIRECT [[Axiom of foundation]]
  59 B (7 words) - 23:19, 8 March 2017
• Axiom of foundation
  422 B (62 words) - 23:23, 8 March 2017

Page text matches

• Basis for a topology
  This pattern occurs a lot, like with the axiom of extensionality in set theory. </ref> - if any 2 basis elements have non
  5 KB (802 words) - 18:35, 17 December 2016
• Set theory axioms
  ! Axiom | For a set {{M|A}} and a property {{M|P}} the set known to exist by axiom 3 is unique, thus we may write <math>\{x\in A|P(x)\}</math> to denote it un
  3 KB (619 words) - 10:25, 11 March 2015
• Motivation for set theory axioms
  From this we could say as an axiom: '''there is only 1 empty set''' - but this is overly-strong (it is indeed ==The axiom of existence==
  3 KB (584 words) - 23:03, 28 February 2015
• Ordered pair
  By the axiom of a pair we may create <math>\{a,b\}</math> and <math>\{a,a\}=\{a\}</math>
  2 KB (327 words) - 07:22, 27 April 2015
• Hausdorff space
  ...al{J})}} we say it is ''Hausdorff''{{rITTBM}} or ''satisfies the Hausdorff axiom'' if:
  4 KB (679 words) - 22:52, 22 February 2017
• Index of set-like notations
  * {{M|\{x\in X\vert p(x)\} }} - relating to axiom schema of comprehension.
  360 B (61 words) - 07:49, 12 March 2016
• Predicate
  * [[Axiom of schema of comprehension]] - This states that given a set {{M|A}} we can
  916 B (160 words) - 18:44, 18 March 2016
• Topological separation axioms
  The {{M|T_i}} notation exists because the German word for "separation axiom" is "Trennungsaxiome"<ref name="ITTGG"/>
  4 KB (569 words) - 00:08, 4 May 2016
• The real numbers
  ...[[axiom of completeness]] - a badly named property that isn't really an [[axiom]]. |content={{:Axiom of completeness/Statement}}}}
  1 KB (200 words) - 21:31, 26 February 2017
• Axiom of completeness
  ...al numbers, although first years are often ''given'' it as if it were an [[axiom]]; it may be proved if one constructs [[the real numbers]] "properly"}} ==[[Axiom of completeness/Statement|Statement]]==
  467 B (69 words) - 13:06, 30 July 2016
• Notes:The foundations of Mathematics - Kunen
  ! Axiom : '''Alec's note: ''' "axiom" 0 can be shown from the axiom of infinity.
  2 KB (342 words) - 02:38, 31 July 2016
• Principle of excluded middle
  {{Stub page|grade=A|msg=This is really an axiom surely.... as (although there'd be not much point to anything otherwise) it
  505 B (79 words) - 10:29, 8 September 2016
• Invariant of an equivalence relation
  ...uivalent conditions to the axiom of choice|equivalent condition to]] the [[axiom of choice]] is that [[every partition has a set of representatives]] that's
  3 KB (478 words) - 18:58, 9 November 2016
• Quotient by an equivalence relation
  * [[Axiom of choice]]
  2 KB (295 words) - 14:16, 13 November 2016
• A monotonically increasing sequence bounded above converges
  ...MonotonicallyIncreasingAndBoundedAboveHasLimit.JPG|thumb|caption]]By the [[axiom of completeness]] any [[set]] of [[real numbers]] with an [[upper bound]] h
  3 KB (493 words) - 07:21, 23 November 2016
• Empty set
  The empty set, denoted {{M|\emptyset}} is posited to exist by an axiom and is the set that contains no elements. It is also a subset of every set
  280 B (46 words) - 11:34, 17 January 2017
• Successor of a set
  At the point which this is usually defined (before the [[Axiom of infinity]]) - even if [[relations]] are covered, and thus [[functions]] ...in A\iff(a\eq x\vee a\eq x)]}} - where equality is understood as per the [[Axiom of extensionality]]
  2 KB (305 words) - 15:14, 3 February 2017
• Inductive set
  * [[The axiom of infinity]] - positing that an inductive set exists.
  924 B (162 words) - 15:56, 3 February 2017
• A pair of identical elements is a singleton
  Let {{M|t}} be a [[set]]. By ''[[the axiom of pairing]]'' we may construct a unique (unordered) pair, which up until n {{XXX|When the paring axiom has a page, do the same thing}}
  2 KB (315 words) - 23:35, 8 March 2017
• Axiom schema of replacement
  The ''axiom schema of replacement'' posits that if {{M|F}} is some [[class function]] t
  2 KB (390 words) - 15:28, 5 April 2017