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• 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
• A pair of identical elements is a singleton
  ...{{M|\{t,t\} }}. We now show that {{M|\{t,t\} }} is a {{link|singleton|set theory}}, thus justifying the notation: ...in\{t,t\}\rightarrow y\eq x)]}} (as per definition of {{link|singleton|set theory}}
  2 KB (315 words) - 23:35, 8 March 2017
• Rewriting for-all and exists within set theory
  ==Notes== {{Theorem Of|Formal Logic|Set Theory}}
  2 KB (358 words) - 17:26, 8 March 2017
• Axiom schema of replacement
  * Apart of what set theories? ...k|image|function}} of {{M|X}} under {{M|F}} - denoted {{M|F(X)}} is also a set{{rSTTJ}}.
  2 KB (390 words) - 15:28, 5 April 2017
• There is no set of all sets
  {{Provisional page|grade=A*|msg=The "core pages" of set theory need to be unified and designed to be viewed in a specific order so all the ...">[[Media:WarwickSetTheoryLectureNotes2011.pdf|Warwick lecture notes - Set Theory - 2011 - Adam Epstein]] - page 6</ref>
  2 KB (330 words) - 01:13, 9 March 2017
• Monotonicity of the integral of non-negative extended-real-valued measurable functions with respect to a measure
  ...A*|msg=Stub, needs review, linking to from other pages, a bit of a measure-theory shuffle}} Let {{M|(X,\mathcal{A},\mu)}} be a [[measure space]] and let {{M|f,g\in}}[[Set of non-negative extended-real-valued measurable functions|{{M|\mathcal{M}_{
  3 KB (623 words) - 19:41, 14 April 2017
• Simply connected topological space
  ...\ (\text{rel }\{0,1\}))\big]}}]] - note [[C(I,X)|{{M|C([0,1],X)}}]] is the set of all {{link|path|topology|s}} into {{M|X}} ==Notes==
  4 KB (601 words) - 16:10, 24 April 2017
• Contractible topological space
  ...we're okay either way.</ref> - where [[C(X,Y)|{{M|C(X,Y)}}]] is simply the set of all [[continuous maps]] from {{M|X}} to {{M|Y}} ==Notes==
  3 KB (544 words) - 20:00, 24 April 2017
• Homotopy equivalent topological spaces
  ** Here [[C(X,Y)|{{M|C(X,Y)}}]] denotes the set of [[continuous maps]] from {{M|X}} and {{M|f\simeq g}} denotes the relatio ==Notes==
  3 KB (596 words) - 21:13, 24 April 2017
• Graph (graph theory)
  * {{M|V}} be a [[finite set]] whose elements we shall call ''vertices'' (singular: ''vertex'') or ''nod * {{M|E}} is a finite set of ''edges'' (singular: ''edge''), which may or may not have data associate
  2 KB (319 words) - 22:15, 13 January 2018
• Digraph
  ...nguages and automata hardbook by my bed, deal with later.</ref> for finite set of vertices {{M|V}} and {{M|E}} are edges of the form {{M|(v_i,v_j)}} - not ==Notes==
  903 B (155 words) - 22:18, 13 January 2018
• Projection matrix
  ...lgebra, the {{plural|canonical projection|s}} of a {{link|product|category theory}} or a [[projector]] matrix. Otherwise we calculate it's shading (to yield colour and such) and then we set the resulting screen coordinate {{M|x,y}} pixel to whatever colour we want
  6 KB (1,051 words) - 07:44, 13 December 2017
• Logical workings of the Enigma machines
  {{Stub page|grade=A*|msg=This page is just some jumbled notes for now, the page will emerge from it with time [[User:Alec|Alec]] ([[User ...ments from the [[permutation group]] {{M|S_{26} }}, {{M|I}} represents the set our permutations operate on, which is 26 unique elements (consider these as
  4 KB (696 words) - 15:24, 15 December 2017
• Distribution of the sample median
  ...in the "notes" stage, and is a staging area from conclusions drawn from [[Notes:Distribution of the sample median]]}} ...ution purely on that foundation, then anything which is itself ordinal (in theory both additive and real units) will be a [[corollary]].
  5 KB (994 words) - 01:22, 16 March 2018
• The integers
  ==Notes== ...ion|Abstract Algebra|Number Theory|Real Analysis|Elementary Set Theory|Set Theory}}
  629 B (90 words) - 13:04, 10 February 2018
• The 2 foundational ways of counting
  ==Relation to set theory== ...he set {{M|A':\eq\{1,\ldots,m\}\subseteq\mathbb{N} }} and with {{M|B}} the set {{M|B':\eq\{1,\ldots,n\}\subseteq\mathbb{N} }} then for:
  1 KB (202 words) - 08:42, 31 August 2018
• The 6 primitives of counting
  ...ly some (''suitable'') notion of decision or choice, to then back with set theory, as the caveats below make clear we need [[User:Alec|Alec]] ([[User talk:Al ==Notes==
  720 B (96 words) - 08:46, 31 August 2018