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• Lower bound
  * [[Infimum]] - the ''greatest'' lower bound of a set. * [[Upper bound]] - the [[dual (order theory)|dual]] concept.
  816 B (140 words) - 07:23, 20 May 2016
• Hereditary sigma-ring generated by
  ...|grade=A*|msg=Needed for progress, I started the page to get some notation set in stone.}} {{Measure theory navbox|plain}}
  877 B (138 words) - 19:24, 24 May 2016
• The set of all mu*-measurable sets is a ring
  {{DISPLAYTITLE:The set of all {{M|\mu^*}}-measurable sets is a ring}}{{Stub page|grade=A*}} {{M|\mathcal{S} }}, [[The set of all mu*-measurable sets|the set of all {{M|\mu^*}} measurable sets]], is a [[ring of sets]]{{rMTH}}.
  8 KB (1,271 words) - 08:36, 29 May 2016
• The set of all mu*-measurable sets is a sigma-ring
  {{Stub page|grade=A*|msg=Currently in the notes stage, see [[Notes:The set of all mu*-measurable sets is a ring]]}} ...0} }} (where {{M|\mathcal{H} }} is a [[hereditary sigma-ring]]) that [[the set of all mu*-measurable sets is a ring]]. It is in fact not only a [[ring of
  521 B (82 words) - 01:01, 30 May 2016
• Group/New page
  Let {{M|G}} be a [[set]] and a [[binary operation]] (a [[function]]) {{M|*:G\times G\rightarrow G} {{Group theory navbox|plain}}
  2 KB (326 words) - 11:38, 2 July 2016
• Group factorisation theorem
  ...play are eligible (satisfy the requirements to factor) for the theorem. We set up as follows: {{Group theory navbox|plain}}
  7 KB (1,195 words) - 22:55, 3 December 2016
• Free monoid generated by
  ...to check [[Discussion of the free monoid and free semigroup generated by a set]], as there are some things to note Given a [[set]], {{M|X}}, there is a ''free'' [[monoid]], {{M|(F,*)}}{{rAAPAG}}.
  2 KB (419 words) - 16:20, 20 July 2016
• Free semigroup generated by
  ...nce, see [[Discussion of the free monoid and free semigroup generated by a set]] ...p) - see [[discussion of the free monoid and free semigroup generated by a set]]){{rAAPAG}}, defined as follows:
  1 KB (200 words) - 07:07, 21 July 2016
• Semigroup
  A semigroup{{rAAPAG}} is a [[tuple]], {{M|(S,*)}}, consisting of a [[set]], {{M|S}} and a [[binary operation]], {{M|*:S\times S\rightarrow S}}, wher {{Semigroup theory navbox|plain}}
  631 B (99 words) - 07:27, 21 July 2016
• Permutation of a set
  : '''Note: ''' [[permutation on a set]] redirects here. Let {{M|X}} be any ''non-empty'' [[set]], {{M|X}}. A ''permutation'' on {{M|X}}{{rRFAGRBJTA}}{{rAAPAG}} is:
  870 B (134 words) - 23:59, 21 July 2016
• Extending pre-measures to measures
  # [[The set of all mu*-measurable sets forms a ring|the set of all {{M|\mu^*}}-measurable sets forms a ring]] # [[The set of all mu*-measurable sets forms a sigma-ring|the set of all {{M|\mu^*}}-measurable sets forms a {{sigma|ring}}]]
  2 KB (257 words) - 17:27, 17 August 2016
• Semi-ring of sets
  ...is almost a measure. A [[ring of sets]] is closed under all the elementary set operations. ...R} }}, Suppose {{M|a<b}} and {{M|c<d}} (as if either interval is the empty set the result is trivial). Suppose they partially intersect with {{M|a<c}} and
  3 KB (508 words) - 17:25, 18 August 2016
• The ring of sets generated by a semi-ring is the set containing the semi-ring and all finite disjoint unions
  ...tion</ref> {{M|\mathcal{F} }}, written {{M|R(\mathcal{F})}} is exactly the set {{M|\mathcal{F} }} and all finite [[union|unions]] of elements of {{M|\math ...e proof of this is easy, as [[the intersection of sets is a subset of each set]] we see {{M|1=A\cap B_i\subseteq B_i}} for each {{M|i}}. As the {{M|B_i}}
  7 KB (1,398 words) - 18:33, 19 August 2016
• A pre-measure on a semi-ring may be extended uniquely to a pre-measure on a ring
  * The ring generated by a semi-ring is exactly the set of all finite disjoint unions of elements from that semiring. # [[the ring of sets generated by a semi-ring is the set containing the semi-ring and all finite disjoint unions]]
  2 KB (390 words) - 22:16, 19 August 2016
• Outer splicing set
  # Unite this with the [[mu*-measurable set]] page, possibly by redirecting it here ...t. It is not a well known term. [[mu*-measurable set|{{M|\mu*}}-measurable set]] redirects here.
  2 KB (378 words) - 22:09, 20 August 2016
• Partial-function
  ...">This is my own term. With total orderings any two elements of underlying set of the relation must be comparable. With a total function, {{M|g}}, {{M|g}} ...} (here {{M|f^{-1}(B)}} denotes the [[pre-image]] of {{M|B}}, which is the set containing all {{M|a\in A}} such that {{M|f}} relates {{M|a}} to a {{M|b\in
  2 KB (462 words) - 22:26, 23 August 2016
• First order language
  {{Provisional page|grade=A|msg=Needed for set theory}} ** {{M|V}} - The set of ({{amcm}}, possibly empty) variable symbols: {{M|x_1,x_2,\ldots,x_n,\ldo
  3 KB (455 words) - 10:45, 8 September 2016
• Domain (FOL)
  ...ty bad that this requires a notion of sets when I want to use this for set theory}} * {{M|M}} is a ''[[non-empty]]'' [[set]] {{Caution|I am studying this for set theory, so something is needed here}}
  4 KB (672 words) - 06:42, 10 September 2016
• Demonstrating why category arrows are best thought of as arrows and not functions
  ...ry|s}} are ''[[finite]]'' {{plural|set|s}} and whose {{link|arrow|category theory|s}}, {{M|\xymatrix{A \ar[r]^f & B} }} are {{plural|function|s}}{{rAITCTHS20 {{Category theory navbox|plain}}
  2 KB (275 words) - 12:29, 15 September 2016
• Homotopy is an equivalence relation on the set of all continuous maps between spaces
  ** Let {{M|C^0(X,Y)}} denote the [[set]] of all [[continuous maps]] of the form {{M|(:X\rightarrow Y)}} {{Homotopy theory navbox|plain}}
  2 KB (272 words) - 23:37, 14 October 2016