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• Books:Notes On Set Theory - Second Edition - Yiannis Moschovakis
  267 B (44 words) - 00:05, 4 February 2017

Page text matches

• 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) ==Notes==
  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
• Index of notation
  ! Notes ! [[Index of 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
• Group
  A group is a set {{M|G}} and an operation <math>*:G\times G\rightarrow G</math>, denoted <ma If the operation is obvious then "Let {{M|G}} be the set of (whatever) and let {{M|(G,+)}} be a group"
  7 KB (1,332 words) - 07:17, 16 October 2016
• Algebra of sets
  * [[Types of set algebras]] ==Notes==
  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
• Measurable space
  {{Refactor notice|grade=A*|msg=Lets get this measure theory stuff sorted. At least the skeleton Given a [[set]], {{M|X}}, and a [[sigma-algebra|{{sigma|algebra}}]], {{M|\mathcal{A}\in\m
  2 KB (248 words) - 13:05, 2 February 2017
• Semi-ring of sets/Definition
  A collection of {{plural|set|s}}, {{M|\mathcal{F} }}<ref group="Note">An F is a bit like an R with an un ...mS_i}}. We require that they be pairwise disjoint AND their union be the [[set difference]] of {{M|S}} and {{M|T}}.</ref> - this doesn't require {{M|S-T\i
  2 KB (337 words) - 17:25, 18 August 2016
• The fundamental group
  {{Definition|Topology|Homotopy Theory}} * <math>\pi_1(X,x_0)</math> denotes the set of [[Homotopy class|homotopy classes]] of [[Paths and loops in a topologica
  3 KB (393 words) - 16:10, 4 November 2016
• Passing to the quotient (function)
  Suppose that {{M|1=w^{-1}(v)}} is [[empty-set|empty]] or contains 2 (or more!) elements, then what do we define {{M|\tild * To see that '''if {{M|f}} is surjective so is {{M|\tilde{f} }} see my notes here:
  8 KB (1,644 words) - 20:49, 11 October 2016
• Types of set algebras
  ==Measure theory perspective== ...e class of sets {{M|\mathcal{A} }} is a collection of subsets from another set {{M|\Omega}}
  3 KB (449 words) - 20:06, 19 August 2016
• Set
  * See [[Notes:Set]] {{Definition|Set Theory}}
  60 B (9 words) - 22:28, 19 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: ==Notes==
  4 KB (680 words) - 00:23, 20 August 2016
• Index of properties
  | {{M|\backslash}}-closed<ref name="PTACC">Probability Theory - A comprehensive course - Second Edition - Achim Klenke</ref> ...{{M|\backslash}}-closed uses {{M|\backslash}} to denote [[Set subtraction|set subtraction]]<ref group="Note">This is because {{M|-}}-closed is not a good
  2 KB (360 words) - 20:43, 15 June 2015
• Class of sets closed under complements properties
  ...a system of subsets of {{M|\Omega}} such that<ref name="PTACC">Probability Theory - A comprehensive course - Achim Klenke</ref>: * [[Types of set algebras]]
  1 KB (165 words) - 20:50, 15 June 2015