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• 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
• 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
• 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
• 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
• 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
• Algebra of sets
  * [[Types of set algebras]] {{Measure theory navbox|plain}}
  3 KB (507 words) - 18:43, 1 April 2016
• Sigma-algebra
  # Show a {{sigma|algebra}} is closed under [[set-subtraction]], {{M|\forall A,B\in\mathcal{A}[A-B\in\mathcal{A}]}} * {{M|\mathcal{A} }} is closed under [[Set subtraction|set subtraction]]
  8 KB (1,306 words) - 01:49, 19 March 2016
• Additive function
  {{Requires references|See Halmos' measure theory book too}} ...ve function (which way have meaning in say algebra), be sure to update the SET FUNCTION redirects that point into this page
  6 KB (971 words) - 18:16, 20 March 2016
• Measure
  A (positive) ''measure'', {{M|\mu}} is a [[set function]] from a [[sigma-ring|{{sigma|ring}}]], {{M|\mathcal{R} }}, to the ...n\right)=\sum_{n=1}^\infty\mu(A_n)]}} ({{M|\mu}} is a [[countably additive set function]])
  6 KB (941 words) - 14:39, 16 August 2016
• Semi-ring of half-closed-half-open intervals
  ...]] of [[set|sets]] where one or more of the {{M|X_\alpha}} are the [[empty set]], {{M|\emptyset}}, then: {{Measure theory navbox|plain}}
  4 KB (680 words) - 00:23, 20 August 2016
• Properties of classes of sets closed under set-subtraction
  Suppose {{M|\mathcal{A} }} is an arbitrary class of [[set|sets]] with the property that: ...=\forall A,B\in\mathcal{A}[A-B\in\mathcal{A}]}} where {{M|A-B}} denotes "[[set subtraction]]" ({{AKA}}: [[relative complement]])
  3 KB (490 words) - 11:38, 21 August 2016
• Site projects:Patrolling measure theory/Task list
  * [[Class of sets closed under set-subtraction properties]] - '''DONE''' [[User:Alec|Alec]] ([[User talk:Alec| * [[Integral (measure theory)]] '''DONE''' [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 02:01, 19 March
  5 KB (645 words) - 11:40, 21 August 2016
• Group action
  A (left) ''group action'' of a [[group]] {{M|(G,*)}} on a [[set]] {{M|X}} is a [[mapping]]{{rAAPAG}}: ** [[The symmetric group on a set acts on the set by evaluation]]
  2 KB (320 words) - 23:28, 21 July 2016
• The (pre-)measure of a set is no more than the sum of the (pre-)measures of the elements of a covering for that set
  ...than the sum of the (pre-)measures of the elements of a covering for that set/Statement|Statement]]== ...than the sum of the (pre-)measures of the elements of a covering for that set/Statement}}
  4 KB (688 words) - 21:03, 31 July 2016
• Set subtraction
  Given two sets, {{M|A}} and {{M|B}} we define ''set subtraction'' ({{AKA}}: ''relative complement''{{rMTH}}) as follows: ==Trivial expressions for set subtraction==
  1 KB (237 words) - 00:48, 21 March 2016
• Pre-measure/New page
  ...ive) pre-measure'' is an ''[[extended real valued]]'' [[countably additive set function]], {{M|\bar{\mu}:\mathcal{R}\rightarrow\overline{\mathbb{R}_{\ge 0 * [[Types of set algebras]]
  3 KB (422 words) - 21:25, 17 August 2016
• Partial ordering
  ...for anything other than denoting [[subset|subsets]], the relation and the set it relates on will go together, so you'll already be using {{M|\subseteq}} A tuple consisting of a set {{M|X}} and a partial order {{M|\sqsubseteq}} in {{M|X}} is called a [[pose
  4 KB (740 words) - 10:11, 20 February 2016
• Strict partial ordering
  ...for anything other than denoting [[subset|subsets]], the relation and the set it relates on will go together, so you'll already be using {{M|\subseteq}} {{Order theory navbox|plain}}
  3 KB (436 words) - 10:15, 20 February 2016
• Overview of partial orders
  A ''partial order'' is a [[relation]] on a set {{M|X}}, which we shall call {{M|\mathcal{R}\subseteq X\times X}} that is{{ {{Order theory navbox|plain}}
  3 KB (454 words) - 07:40, 11 April 2016
• SET (category)
  ...ts]] and every [[function]] (in the conventional sense, as mappings from 1 set to another) between those sets as the [[arrows of a category|arrows of the * '''Note: ''' sometimes the {{M|\mathrm{SET} }} category is {{AKA}} {{M|\mathrm{SETS} }} (and the page <code>[[SETS (ca
  1 KB (168 words) - 10:05, 19 February 2016