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304 B (43 words) - 13:57, 2 June 2016
- ...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
- The ''axiom schema of replacement'' posits that if {{M|F}} is some [[class function]] t2 KB (390 words) - 15:28, 5 April 2017
- #REDIRECT [[Axiom schema of replacement]]67 B (8 words) - 23:18, 8 March 2017
- #REDIRECT [[Axiom of foundation]]59 B (7 words) - 23:19, 8 March 2017
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422 B (62 words) - 23:23, 8 March 2017
Page text matches
- This pattern occurs a lot, like with the axiom of extensionality in set theory. </ref> - if any 2 basis elements have non5 KB (802 words) - 18:35, 17 December 2016
- ! 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 un3 KB (619 words) - 10:25, 11 March 2015
- 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
- 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
- ...al{J})}} we say it is ''Hausdorff''{{rITTBM}} or ''satisfies the Hausdorff axiom'' if:4 KB (679 words) - 22:52, 22 February 2017
- * {{M|\{x\in X\vert p(x)\} }} - relating to axiom schema of comprehension.360 B (61 words) - 07:49, 12 March 2016
- * [[Axiom of schema of comprehension]] - This states that given a set {{M|A}} we can916 B (160 words) - 18:44, 18 March 2016
- 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
- ...[[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
- ...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 : '''Alec's note: ''' "axiom" 0 can be shown from the axiom of infinity.2 KB (342 words) - 02:38, 31 July 2016
- {{Stub page|grade=A|msg=This is really an axiom surely.... as (although there'd be not much point to anything otherwise) it505 B (79 words) - 10:29, 8 September 2016
- ...uivalent conditions to the axiom of choice|equivalent condition to]] the [[axiom of choice]] is that [[every partition has a set of representatives]] that's3 KB (478 words) - 18:58, 9 November 2016
- * [[Axiom of choice]]2 KB (295 words) - 14:16, 13 November 2016
- ...MonotonicallyIncreasingAndBoundedAboveHasLimit.JPG|thumb|caption]]By the [[axiom of completeness]] any [[set]] of [[real numbers]] with an [[upper bound]] h3 KB (493 words) - 07:21, 23 November 2016
- 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 set280 B (46 words) - 11:34, 17 January 2017
- 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
- * [[The axiom of infinity]] - positing that an inductive set exists.924 B (162 words) - 15:56, 3 February 2017
- 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
- The ''axiom schema of replacement'' posits that if {{M|F}} is some [[class function]] t2 KB (390 words) - 15:28, 5 April 2017