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Create the page "Set Theory" on this wiki! See also the search results found.

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• Set theory axioms
  ...sed to provide some discussion for the axioms (for example "there exists a set with no elements" doesn't really deserve its own page) ...Only "major" results are shown, they are covered in the motivation for set theory page, and "D" denotes "definition" - which is something that is natural to
  3 KB (619 words) - 10:25, 11 March 2015
• Motivation for set theory axioms
  ...s. For example you are happy that {{M|\{1,2,3\}=\{2,1,3\} }} and that this set (I use singular because they are identical) contains the elements {{M|1}}, ...- for example we use a letter (<math>\emptyset</math>) to denote the empty set, what if there are 2 empty sets? We would like to justify this.
  3 KB (584 words) - 23:03, 28 February 2015
• Books:Set Theory - Thomas Jech - Third millennium edition, revised and expanded
  267 B (42 words) - 15:42, 31 December 2015
• Site projects:Split set theory into elementary set theory
  ...this way pages tagged as elementary set theory have no business in the set theory category. * Create an "elementary set theory" subject in the [[Site:Mathematical subject index]]
  739 B (114 words) - 12:21, 9 April 2016
• Types of set algebras/Measure theory summary table
  ...from a search engine you don't want this sub-page, but the page [[types of set algebras]] instead''' ==Measure theory perspective summary table==
  559 B (79 words) - 20:05, 19 August 2016
• Index of elementary set theory equalities
  [[Category:Index]]{{Theorem Of|Elementary Set Theory|Set Theory}}
  497 B (85 words) - 14:46, 31 January 2017
• Books:Introduction To Set Theory - Third Edition, Revised and Expanded - Karel Hrbacek & Thomas Jech
  267 B (44 words) - 12:54, 3 February 2017
• Books:Notes On Set Theory - Second Edition - Yiannis Moschovakis
  267 B (44 words) - 00:05, 4 February 2017
• Singleton (set theory)/Definition
  ...">[[Media:WarwickSetTheoryLectureNotes2011.pdf|Warwick lecture notes - Set Theory - 2011 - Adam Epstein]] - page 2.75.</ref>: ...X[t\eq s]}}<ref group="Note">see [[rewriting for-all and exists within set theory]]</ref>
  1 KB (219 words) - 23:34, 8 March 2017
• Singleton (set theory)
  Notice that we have manage to define a set containing one thing without any notion of the number 1. #* By "''[[rewriting for-all and exists within set theory]]''" we see:
  1 KB (192 words) - 17:38, 8 March 2017
• Rewriting for-all and exists within set theory
  {{Theorem Of|Formal Logic|Set Theory}}
  2 KB (358 words) - 17:26, 8 March 2017

Page text matches

• Main Page
  * [[Set Theory]] * [[Measure Theory]]
  7 KB (999 words) - 16:51, 11 May 2020
• Bijection
  ...(X)</math> where <math>\mathcal{P}(X)</math> denotes the [[Power set|power set]] of <math>X</math>) {{Definition|Set Theory|Elementary Set Theory}}
  732 B (124 words) - 11:49, 26 September 2016
• Injection
  ...rjection/injection/[[bijection]] to be seen through the lens of [[Category Theory]]. [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 21:50, 8 May 2018 (UTC) ...ijection where the cardinality is always 1 (and thus we take the singleton set <math>f^{-1}(y)=\{x\}</math> as the value it contains, writing {{M|1=f^{-1}
  3 KB (463 words) - 21:50, 8 May 2018
• Surjection
  {{Definition|Set Theory}}
  2 KB (263 words) - 21:56, 8 May 2018
• The relationship between logical implication and the subset relation
  ...n A\implies x\in B]</math><ref>Definition 3.10 (p10) - Introduction to Set Theory, Third Edition (Revised and Expanded) - Karel Hrbacek and Thomas Jech</ref> This is easily seen to be equivalent as if {{M|A}} is [[empty set|empty]] (so there is no {{M|x\in A}} to speak of) the implication is semant
  776 B (136 words) - 17:36, 16 January 2017
• Basis for a topology
  ...but "let {{M|A\in\mathcal{P}(B)}}" instead. To emphasise that the [[power-set]] is possibly in play. ...se]], we usually deal with subsets of the ''space'' not subsets of the ''[[set system]]'' on that space.<br/>
  5 KB (802 words) - 18:35, 17 December 2016
• The intersection of sets is a subset of each set
  {{Theorem Of|Set Theory}}
  820 B (159 words) - 21:35, 15 August 2015
• Commutativity of intersection
  {{Theorem Of|Set Theory}}
  610 B (122 words) - 19:32, 28 October 2016
• Measure space
  ...t, and {{M|\mathcal{A} }} is a [[Sigma-algebra|{{Sigma|algebra}}]] on that set (which together, as {{M|(X,\mathcal{A})}}, form a [[Measurable space|measur Given a set {{M|X}} and an [[Algebra of sets|algebra]], {{M|\mathcal{A} }} (NOT a {{sig
  1 KB (188 words) - 15:24, 21 July 2015
• Function
  {{Definition|Set Theory}}
  4 KB (659 words) - 13:01, 19 February 2016
• Set theory axioms
  ...sed to provide some discussion for the axioms (for example "there exists a set with no elements" doesn't really deserve its own page) ...Only "major" results are shown, they are covered in the motivation for set theory page, and "D" denotes "definition" - which is something that is natural to
  3 KB (619 words) - 10:25, 11 March 2015
• Motivation for set theory axioms
  ...s. For example you are happy that {{M|\{1,2,3\}=\{2,1,3\} }} and that this set (I use singular because they are identical) contains the elements {{M|1}}, ...- for example we use a letter (<math>\emptyset</math>) to denote the empty set, what if there are 2 empty sets? We would like to justify this.
  3 KB (584 words) - 23:03, 28 February 2015
• Relation
  ** For example {{M|<}} is a relation in the set of {{M|\mathbb{Z} }} (the integers) ! Set relation
  4 KB (762 words) - 20:07, 20 April 2016
• Ordered pair
  The axioms may be found [[Set theory axioms|here]] ...know <math>\{\{a\}\}=\{\{a'\},\{a',b'\}\}</math> so again using the [[Set theory axioms]] (namely Extensionality) we see <math>a=a'=b'</math> so <math>a=a'<
  2 KB (327 words) - 07:22, 27 April 2015
• The domain, range and field of a relation exist
  ...>\{x|\exists y:(x,y)\in R\}</math> exists, to do this we require the [[Set theory axioms|axioms]] of schema and union. {{Theorem Of|Set Theory}}
  339 B (63 words) - 07:22, 27 April 2015
• Todo list
  | Proof that a function is invertible {{M|\iff}} it is one-to-one (Jech, Set Theory -p25) | Proof that <math>B^A</math> - the set of all functions from {{M|A}} into {{M|B}} exists
  464 B (76 words) - 16:54, 10 June 2015
• Ordering
  {{Definition|Set Theory}}
  5 KB (1,006 words) - 13:21, 1 January 2016
• Equivalence relation
  * An [[equivalence class]] is the name given to the set of all things which are equivalent under a given equivalence relation. **[[The equivalence classes of an equivalence relation partitions a set]].
  3 KB (522 words) - 15:18, 12 February 2019
• Index of notation
  ! [[Index of set-like notations]] | set-like notations
  9 KB (1,490 words) - 06:13, 1 January 2017
• Sequence
  ...>\{a_n\}_{n=1}^\infty</math> however I don't like this, as it looks like a set. I have seen the notation <math>(a_n)_{n=1}^\infty</math> and I must say I ...Maurin</ref>, <math>f:\mathbb{N}\rightarrow S</math> where {{M|S}} is some set. For a finite sequence it is simply <math>f:\{1,...,n\}\rightarrow S</math>
  2 KB (419 words) - 18:12, 13 March 2016