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• Category Theory (subject)
  '''Category theory is the study of objects linked by arrows, where arrows compose'''. In fact ...most familiar category to the reader will be [[SET (category)|{{M|\mathrm{SET} }}]]
  2 KB (311 words) - 11:46, 19 February 2016
• Preorder
  A ''preorder'', {{M|\preceq}}, on a set {{M|X}} is a [[relation]] in {{M|X}}, so {{M|\preceq\subseteq X\times X}}, A tuple, consisting of a set {{M|X}}, equipped with a preorder {{M|\preceq}} is called a ''[[preset]]''<
  2 KB (355 words) - 10:13, 20 February 2016
• Preset
  A ''preset'' is a [[tuple]] consisting of a [[set]] {{M|X}} and a [[preorder]] on {{M|X}}, {{M|\preceq}}{{rAITCTHS2010}}, the * [[Poset]] - the term for a set equipped with a [[partial ordering]] on itself.
  436 B (66 words) - 16:54, 1 March 2016
• Order Theory (subject)
  ...from various kinds of orderings, called [[Lattice Theory (subject)|lattice theory]]. Some order theory is desired for parts of [[Analysis (subject)|analysis]], for this I recomme
  2 KB (217 words) - 15:26, 26 February 2016
• Exists functor
  ...] taking [[SET (category)|{{M|\mathrm{SET} }}]] {{M|\leadsto}} {{M|\mathrm{SET} }} defined as follows{{rAITCTHS2010}}: ...A\mapsto\mathcal{P}(A)]}}, recall {{M|\mathcal{P}(X)}} denotes the [[power set]] of {{M|X}}
  2 KB (317 words) - 17:51, 13 March 2016
• Upper section
  ...r I am dealing with [[preset|presets]] not [[poset|posets]] here, so upper set might only be for posets, and upper section for presets, or both. Not sure * [[Lower section]] - the [[dual (order theory)|dual]] concept to this
  1 KB (171 words) - 16:35, 20 February 2016
• Index of operators on ordered sets
  If you are given a set, say {{M|X}} and any of a: on that set, then this page indexes various operators that might take such a structured
  2 KB (304 words) - 17:01, 20 February 2016
• TOP (category)
  ...ological space|topological spaces]], the objects are [[tuple|tuples]] of a set {{M|X}} and a topology {{M|\mathcal{J}_X}} on {{M|X}} and the arrows, or mo {{Todo|Discuss as a subcategory of {{M|\mathrm{SET} }}, remember it must first go under the [[forgetful functor]] to discard t
  971 B (139 words) - 20:10, 20 February 2016
• Measure Theory (subject)
  ...engths, so given a set where you can do these things (subtract and add - [[set subtraction]] and [[union]] respectively) you expect to be able to define a The measure theory project contains:
  832 B (121 words) - 15:24, 26 February 2016
• Predicate
  ...dicate'', {{M|P}}, is a [[n-place relation|{{M|1}}-place relation]] on a [[set]] {{M|X}}<ref group="Note">{{M|P\subseteq X}} in this case. In contrast to ...comprehension]] - This states that given a set {{M|A}} we can construct a set {{M|B}} such that {{M|1=B=\{x\in A\ \vert P(x)\} }} for some ''predicate''
  916 B (160 words) - 18:44, 18 March 2016
• Symmetric difference
  Let {{M|A,B\in\mathcal{P}(X)}} be two [[subset|subsets]] of a [[set]] {{M|X}}. We define the ''symmetric difference'' of {{M|A}} and {{M|B}} as ...A\triangle B:=(A-B)\cup(B-A)}}<ref group="Note">Here {{M|A-B}} denotes ''[[set subtraction]]''.</ref>
  830 B (139 words) - 00:59, 21 March 2016
• Hereditary system of sets
  {{Stub page|Needs linking to where it is used, notes on a sort of "power-set" like construct.|grade=B}} ...in [[Measure Theory (subject)|Measure Theory]] and ''[[Hereditary (measure theory)]]'' redirects here
  793 B (125 words) - 21:25, 19 April 2016
• Hereditary sigma-ring
  ...rties. Additionally the "use" section requires expansion. Comment on power-set and sigma-algebra special case. Find out about related term, {{sigma|ideal} ...{{M|\mathcal{H} }}, is a system of sets that is both [[hereditary (measure theory)|hereditary]] and a [[sigma-ring|{{sigma|ring}}]]{{rMTH}}. This means {{M|\
  1 KB (220 words) - 21:25, 19 April 2016
• Monotonic
  ...ires references|Find an order theory book, also I think that huge category theory PDF (Harold Simmons) has it}} # Unite with [[monotonic set function]]
  1 KB (190 words) - 04:50, 9 April 2016
• Extension
  {{Function terminology navbox|plain}} {{Definition|Set Theory}}[[Category:Function Terminology]]
  575 B (89 words) - 20:02, 8 April 2016
• Restriction
  ...l{P}(X)}}<ref group="Note">Recall {{M|\mathcal{P}(X)}} denotes the [[power-set]] of {{M|X}}</ref> (so {{M|A\subseteq X}} - and is any subset) we define a {{Function terminology navbox|plain}}
  652 B (107 words) - 20:01, 8 April 2016
• Extending pre-measures to outer-measures
  ...infty A_n\right\} }} - here {{M|\text{inf} }} denotes the [[infimum]] of a set. ...than the sum of the (pre-)measures of the elements of a covering for that set]], which states, symbolically:
  11 KB (1,921 words) - 16:59, 17 August 2016
• Greater than or equal to
  {{Order theory navbox|plain}} {{Relations navbox}}
  1 KB (152 words) - 15:56, 9 April 2016
• Infimum
  ...athcal{P}(X)}} where {{M|\mathcal{P}(S)}} denotes the [[power set]] of a [[set]] {{M|S}}</ref>. The ''infimum'' ({{AKA}}: ''greatest lower bound'', ''g.l. ...ce{\left\{x\in X\ \vert\ (\forall a\in A[x\preceq a])\right\} }_{\text{the set of all lower bounds of }A }\Big[b\preceq\text{Inf}(A)\Big]}} - which states
  5 KB (851 words) - 08:55, 29 July 2016
• Upper bound
  * [[Supremum]] - the ''lowest'' upper bound of a set. * [[Lower bound]] - the [[dual (order theory)|dual]] concept.
  813 B (140 words) - 07:23, 20 May 2016