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• Power set
  In [[set theory]], the '''power set''' of a set ''X'' is the set of all [[subset]]s of ''X''. The power set is [[order (relation)|ordered]] by [[inclusion (set theory)|inclusion]], ma
  317 bytes (49 words) - 14:28, 14 March 2021
• Power set/Definition
  74 bytes (12 words) - 14:32, 28 November 2008
• Power set/Bibliography
  611 bytes (74 words) - 12:55, 30 November 2008
• Power set/Related Articles
  881 bytes (141 words) - 14:33, 28 November 2008

Page text matches

• Power set
  In [[set theory]], the '''power set''' of a set ''X'' is the set of all [[subset]]s of ''X''. The power set is [[order (relation)|ordered]] by [[inclusion (set theory)|inclusion]], ma
  317 bytes (49 words) - 14:28, 14 March 2021
• Power (disambiguation)
  {{rpl|Power set}}
  1 KB (178 words) - 13:34, 24 January 2023
• Cantor's diagonal argument/Related Articles
  {{r|Power set}}
  307 bytes (44 words) - 16:27, 26 July 2008
• Subset
  The [[power set]] of ''X'' is the set of all subsets of ''X''.
  596 bytes (101 words) - 12:42, 30 December 2008
• Set theory/Related Articles
  {{r|Power set}}
  477 bytes (65 words) - 07:22, 22 July 2011
• Sigma algebra
  ...tyle \Omega</math>, let <math>\scriptstyle P\,=\, 2^\Omega</math> be its [[power set]], i.e. set of all [[subset]]s of <math>\Omega</math>. * For any set ''S'', the power set 2^''S'' itself is a &sigma; algebra.
  2 KB (314 words) - 16:35, 27 November 2008
• Subset/Related Articles
  {{r|Power set}}
  914 bytes (146 words) - 13:36, 28 November 2008
• Filter (mathematics)
  Formally, a filter on a set ''X'' is a subset <math>\mathcal{F}</math> of the power set <math>\mathcal{P}X</math> with the properties:
  2 KB (297 words) - 17:47, 1 December 2008
• Cantor's diagonal argument
  ...thbb{N}}</math> of subsets of the [[natural number]]s (also known as its [[power set]]) is not [[countable set|countable]]. More generally, it is a recurring th If power set is countable, there is a bijective map <math>F : \mathbb{N} \rightarrow 2^{
  4 KB (745 words) - 23:17, 25 October 2013
• Closure operator
  A ''closure operator'' on a set ''X'' is a function ''F'' on the [[power set]] of ''X'', <math>F : \mathcal{P}X \rarr \mathcal{P}X</math>, satisfying:
  2 KB (414 words) - 03:00, 14 February 2010
• Zermelo-Fraenkel axioms
  *5. <u>Axiom of power set</u>: For any ''X'' there exists a set ''Y''=''P(X)'', the set of all subset
  3 KB (512 words) - 17:28, 2 July 2011
• Hutchinson operator
  ...''X'' to itself. We may regard this as defining an operator ''H'' on the power set '''P''' ''X'' as
  2 KB (327 words) - 15:52, 27 October 2008
• Oxford University Press/Related Articles
  {{r|Power set}}
  1 KB (187 words) - 19:18, 11 January 2010
• Schröder-Bernstein theorem
  on the power set of ''A'' is monotone increasing (2) &sigma; is a monotone increasing function on the power set of ''A'':
  8 KB (1,281 words) - 15:39, 23 September 2013
• Schröder-Bernstein theorem/Citable Version
  on the power set of ''A'' is monotone increasing (2) &sigma; is a monotone increasing function on the power set of ''A'':
  8 KB (1,275 words) - 15:34, 23 September 2013
• Set (mathematics)
  ...may be some complexity in discussing its subsets.) If ''A'' is a set, the power set of ''A'' often is denoted as {{nowrap|℘(''A'')}} or ''P(A)'' or <math>\ma ...of '''''all''''' sets" leads to a contradiction (it cannot include its own power set).<ref name=Craig/> Some sets include themselves (so-called ''impredicative'
  17 KB (2,828 words) - 10:37, 24 July 2011
• Set theory/Citable Version
  ==== Power set ==== ...t of base set: No one-to-one correspondence exists between the set and its power set. Cantor proved that this in fact holds for any set (Cantor's Theorem). This
  22 KB (3,815 words) - 15:46, 23 September 2013
• Function (mathematics)
  ...'push-forward''' of ''f'' is the function <math>f_\vdash</math> from the [[power set]] of ''X'' to that of ''Y'' which maps a subset ''A'' of ''X'' to its image ...the function <math>f^\dashv</math> from the [[power set]] of ''Y'' to the power set of ''X'' which maps a subset ''B'' of ''Y'' to its pre-image in ''X'':
  15 KB (2,342 words) - 06:26, 30 November 2011
• Set theory
  ==== Power set ==== ...t of base set: No one-to-one correspondence exists between the set and its power set. Cantor proved that this in fact holds for any set (Cantor's Theorem). This
  24 KB (4,193 words) - 15:48, 23 September 2013
• Super Chief
  The first motive power set on ''Super Chief-1'' consisted of a pair of blunt-nosed, diesel-electric un
  34 KB (4,986 words) - 11:31, 1 October 2014