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  • Set theory
    ...out to be a tricky matter. However, some unproblematic examples from naïve set theory will make the concept clearer. These examples will be used throughout this == History of set theory ==
    24 KB (4,193 words) - 15:48, 23 September 2013
  • Union (set theory)
    19 bytes (2 words) - 13:25, 23 November 2008
  • Set theory/Definition
    135 bytes (15 words) - 06:12, 22 October 2013
  • Intersection (set theory)
    26 bytes (2 words) - 14:14, 23 November 2008
  • Set theory/Bibliography
    Paul R. Halmos, ''Naive Set Theory.'' <br>&nbsp;&nbsp;''A detailed informal introduction based on ZF set theory.''
    743 bytes (103 words) - 10:26, 10 July 2011
  • Complement (set theory)
    In [[set theory]], the '''complement''' of a [[subset]] of a given [[set (mathematics)|set] In some version of set theory it is common to postulate a "universal set" <math>\mathcal{U}</math> and re
    805 bytes (135 words) - 13:24, 28 November 2008
  • Set theory/Approval
    710 bytes (65 words) - 15:53, 30 May 2010
  • Inclusion (set theory)
    20 bytes (2 words) - 12:20, 30 November 2008
  • Fibre (set theory)
    34 bytes (5 words) - 12:47, 13 December 2008
  • Set theory/Related Articles
    {{r|Naive set theory}} {{r|Axiomatic set theory}}
    477 bytes (65 words) - 07:22, 22 July 2011
  • Complement (set theory)/Definition
    139 bytes (22 words) - 13:28, 28 November 2008
  • Set theory/Citable Version
    ...out to be a tricky matter. However, some unproblematic examples from naïve set theory will make the concept clearer. These examples will be used throughout this == History of set theory ==
    22 KB (3,815 words) - 15:46, 23 September 2013
  • Set theory/External Links
    *A summary of basic facts about sets is found at: {{cite web |title=Basic set theory |url=http://www.illc.uva.nl/~seop/entries/set-theory/primer.html |work=Stan ...ng overview of set theory and its evolution is found at: {{cite web||title=Set theory |url=http://www.illc.uva.nl/~seop/entries/set-theory/index.html |work=Stanf
    865 bytes (130 words) - 09:37, 4 July 2011
  • Inclusion (set theory)/Definition
    94 bytes (12 words) - 12:32, 30 November 2008
  • Fibre (set theory)/Definition
    127 bytes (21 words) - 13:07, 13 December 2008
  • Complement (set theory)/Related Articles
    {{r|Set theory}}
    912 bytes (145 words) - 13:30, 28 November 2008

Page text matches

  • Set theory/Bibliography
    Paul R. Halmos, ''Naive Set Theory.'' <br>&nbsp;&nbsp;''A detailed informal introduction based on ZF set theory.''
    743 bytes (103 words) - 10:26, 10 July 2011
  • 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]], making it a [[lattice (order)|lattice]].
    317 bytes (49 words) - 14:28, 14 March 2021
  • Empty set/Definition
    In set theory, this is a set without elements, usually denoted <math>\{~\}</math> or <mat
    184 bytes (29 words) - 01:06, 19 February 2009
  • Ordered set/Definition
    A [[set theory|set]] with an [[order relation]]
    83 bytes (11 words) - 10:23, 15 July 2011
  • Cardinal number/Related Articles
    {{r|Set theory}}
    370 bytes (47 words) - 17:50, 26 June 2009
  • Axiom of choice/Definition
    Set theory assertion that if S is a set of disjoint, non-empty sets, then there exists
    182 bytes (30 words) - 08:45, 27 November 2011
  • Continuum hypothesis/Related Articles
    {{r|set theory}} {{r|history of set theory}}
    206 bytes (26 words) - 16:28, 11 June 2009
  • Set theory/Related Articles
    {{r|Naive set theory}} {{r|Axiomatic set theory}}
    477 bytes (65 words) - 07:22, 22 July 2011
  • Singleton set
    In [[set theory]], a '''singleton''' is a [[set (mathematics)|set]] with exactly one elemen
    199 bytes (28 words) - 12:58, 7 February 2009
  • Zermelo-Fraenkel axioms/Bibliography
    ...aCUXZip3bN0C&pg=PA337 |pages=pp. 337 ''ff'' |chapter=The axiomatization of set theory |isbn=0816634602 |year=2003 |publisher=University of Minnesota Press}} *{{cite book |title=Introduction to set theory |author=Karel Hrbacek, Thomas J. Jech |edition=3rd ed |url=http://books.goo
    764 bytes (113 words) - 09:14, 16 May 2011
  • Complement (set theory)
    In [[set theory]], the '''complement''' of a [[subset]] of a given [[set (mathematics)|set] In some version of set theory it is common to postulate a "universal set" <math>\mathcal{U}</math> and re
    805 bytes (135 words) - 13:24, 28 November 2008
  • Category theory/Related Articles
    {{r|Class (set theory)|Class}}
    648 bytes (83 words) - 10:12, 11 May 2009
  • Set (mathematics)/Related Articles
    {{r|Set theory}} {{r|Naive set theory}}
    507 bytes (65 words) - 07:17, 22 July 2011
  • Fuzzy subalgebra/Definition
    A chapter of fuzzy set theory.
    67 bytes (9 words) - 08:05, 4 September 2009
  • Zermelo-Fraenkel axioms/External Links
    *A summary of basic facts about sets is found at: {{cite web |title=Basic set theory |url=http://www.illc.uva.nl/~seop/entries/set-theory/primer.html |work=Stan ...ng overview of set theory and its evolution is found at: {{cite web||title=Set theory |url=http://www.illc.uva.nl/~seop/entries/set-theory/index.html |work=Stanf
    865 bytes (130 words) - 17:17, 2 July 2011
  • Set theory/External Links
    *A summary of basic facts about sets is found at: {{cite web |title=Basic set theory |url=http://www.illc.uva.nl/~seop/entries/set-theory/primer.html |work=Stan ...ng overview of set theory and its evolution is found at: {{cite web||title=Set theory |url=http://www.illc.uva.nl/~seop/entries/set-theory/index.html |work=Stanf
    865 bytes (130 words) - 09:37, 4 July 2011
  • Sigma algebra
    # If <math>\scriptstyle A\,\in\, F </math> then the [[complement (set theory)|complement]] <math>\scriptstyle A^c \in F</math> [[Set theory]]
    2 KB (314 words) - 16:35, 27 November 2008
  • Discrete mathematics/Related Articles
    {{r|Set theory}}
    245 bytes (29 words) - 09:38, 18 June 2009
  • Partition (mathematics)
    In [[mathematics]], '''partition''' refers to two related concepts, in [[set theory]] and [[number theory]]. ==Partition (set theory)==
    2 KB (336 words) - 07:17, 16 January 2009
  • Fuzzy control
    '''Fuzzy control''' is the main success of fuzzy set theory and it is devoted to useful applications.
    472 bytes (59 words) - 23:34, 14 February 2010
  • Cantor's diagonal argument/Related Articles
    {{r|Set theory}}
    307 bytes (44 words) - 16:27, 26 July 2008
  • Schröder-Bernstein theorem/Definition
    A classic theorem of set theory asserting that sets can be ordered by size.
    111 bytes (17 words) - 17:30, 24 September 2010
  • Cardinal number/Bibliography
    ...h J. Devlin | authorlink=Keith Devlin | title=Fundamentals of Contemporary Set Theory | series=Universitext | publisher=[[Springer-Verlag]] | year=1979 | isbn=0- * {{cite book | author=Paul Halmos | authorlink=Paul Halmos | title=Naive set theory | series=The University Series in Undergraduate Mathematics | publisher=[[V
    1 KB (146 words) - 17:50, 26 June 2009
  • Subset
    In [[set theory]], a '''subset''' of a [[set (mathematics)|set]] ''X'' is a set ''A'' whose
    596 bytes (101 words) - 12:42, 30 December 2008
  • Zermelo-Fraenkel axioms/Definition
    ...veral possible formulations of [[Set_theory#Axiomatic_set_theory|axiomatic set theory]].
    132 bytes (17 words) - 15:22, 11 May 2011
  • Characteristic function
    In [[set theory]], the '''characteristic function''' or '''indicator function''' of a [[sub
    2 KB (242 words) - 02:01, 2 February 2009
  • Aleph-0
    However, the term "aleph-0" is mainly used in the context of [[set theory]]; which finally turned out to be independent of the axioms of set theory:
    1 KB (214 words) - 13:35, 6 July 2009
  • Georg Cantor/Definition
    ...ages}}</noinclude>(1845-1918) Danish-German mathematician who introduced [[set theory]] and the concept of [[transcendental number]]s
    150 bytes (17 words) - 13:07, 16 March 2011
  • Cocountable topology
    ...open set]]s are those which have [[countable set|countable]] [[complement (set theory)|complement]], together with the empty set. Equivalently, the [[closed set
    1,004 bytes (134 words) - 22:48, 17 February 2009
  • Cofinite topology
    ...the [[open set]]s are those which have [[finite set|finite]] [[complement (set theory)|complement]], together with the empty set. Equivalently, the [[closed set
    1,007 bytes (137 words) - 22:52, 17 February 2009
  • Pointed set
    In [[set theory]], a '''pointed set''' is a [[set (mathematics)|set]] together with a disti
    1 KB (168 words) - 12:06, 22 November 2008
  • Schröder-Bernstein property/Definition
    ...ties that have the same structure as the [[Schröder-Bernstein theorem]] of set theory.
    166 bytes (23 words) - 18:06, 25 September 2010
  • Subset/Related Articles
    {{r|Set theory}} {{r|Complement (set theory)}}
    914 bytes (146 words) - 13:36, 28 November 2008
  • Non-Borel set/Related Articles
    {{r|descriptive set theory}}
    217 bytes (31 words) - 10:31, 21 June 2009
  • Countable set/Bibliography
    * {{cite book | author=Paul Halmos | authorlink=Paul Halmos | title=Naive set theory | series=The University Series in Undergraduate Mathematics | publisher=[[V ...h J. Devlin | authorlink=Keith Devlin | title=Fundamentals of Contemporary Set Theory | series=Universitext | publisher=[[Springer-Verlag]] | year=1979 | isbn=0-
    611 bytes (74 words) - 12:28, 2 November 2008
  • Power set/Bibliography
    ...h J. Devlin | authorlink=Keith Devlin | title=Fundamentals of Contemporary Set Theory | series=Universitext | publisher=[[Springer-Verlag]] | year=1979 | isbn=0- * {{cite book | author=Paul Halmos | authorlink=Paul Halmos | title=Naive set theory | series=The University Series in Undergraduate Mathematics | publisher=[[V
    611 bytes (74 words) - 12:55, 30 November 2008
  • Order (relation)/Bibliography
    ...h J. Devlin | authorlink=Keith Devlin | title=Fundamentals of Contemporary Set Theory | series=Universitext | publisher=[[Springer-Verlag]] | year=1979 | isbn=0- * {{cite book | author=Paul Halmos | authorlink=Paul Halmos | title=Naive set theory | series=The University Series in Undergraduate Mathematics | publisher=[[V
    1 KB (135 words) - 16:24, 4 January 2009
  • Relation (mathematics)/Bibliography
    ...h J. Devlin | authorlink=Keith Devlin | title=Fundamentals of Contemporary Set Theory | series=Universitext | publisher=[[Springer-Verlag]] | year=1979 | isbn=0- * {{cite book | author=Paul Halmos | authorlink=Paul Halmos | title=Naive set theory | series=The University Series in Undergraduate Mathematics | publisher=[[V
    649 bytes (78 words) - 17:27, 3 November 2008
  • Cartesian product/Bibliography
    ...h J. Devlin | authorlink=Keith Devlin | title=Fundamentals of Contemporary Set Theory | series=Universitext | publisher=[[Springer-Verlag]] | year=1979 | isbn=0- * {{cite book | author=Paul Halmos | authorlink=Paul Halmos | title=Naive set theory | series=The University Series in Undergraduate Mathematics | publisher=[[V
    649 bytes (78 words) - 17:30, 3 November 2008
  • Intersection
    In [[set theory]], the '''intersection''' of two sets is the set of elements that they have * {{cite book | author=Paul Halmos | authorlink=Paul Halmos | title=Naive set theory | series=The University Series in Undergraduate Mathematics | publisher=[[V
    2 KB (284 words) - 14:24, 28 November 2008
  • Filter (mathematics)
    In [[set theory]], a '''filter''' is a family of [[subset]]s of a given set which has prope ...bseteq X</math> either <math>A \in \mathcal{F}</math> or the [[complement (set theory)|complement]] <math>X \setminus A \in \mathcal{F}</math>.
    2 KB (297 words) - 17:47, 1 December 2008
  • Non-Borel set
    requires advanced results from [[descriptive set theory]].
    2 KB (252 words) - 11:44, 2 December 2010
  • Union
    In [[set theory]], '''union''' (denoted as ∪) is a set operation between two sets that fo * {{cite book | author=Paul Halmos | authorlink=Paul Halmos | title=Naive set theory | series=The University Series in Undergraduate Mathematics | publisher=[[V
    2 KB (264 words) - 17:13, 4 November 2008
  • Function (mathematics)/Bibliography
    ...h J. Devlin | authorlink=Keith Devlin | title=Fundamentals of Contemporary Set Theory | series=Universitext | publisher=[[Springer-Verlag]] | year=1979 | isbn=0- * {{cite book | author=Paul Halmos | authorlink=Paul Halmos | title=Naive set theory | series=The University Series in Undergraduate Mathematics | publisher=[[V
    774 bytes (96 words) - 02:14, 11 November 2008
  • Finite set
    A characteristic property of finite sets (which, in [[set theory]] is used to ''define'' finite sets) is the following:
    1 KB (222 words) - 16:36, 4 January 2013
  • Inclusion (disambiguation)
    {{r|Inclusion (set theory)}}
    108 bytes (14 words) - 11:04, 31 May 2009
  • Countable set/Related Articles
    {{r|Set theory}}
    267 bytes (32 words) - 19:16, 17 June 2009
  • Axiom of choice
    ...s and [[Kurt Gödel]] showed that it was independent of the other axioms of set theory.
    2 KB (266 words) - 13:28, 5 January 2013
  • Ordered pair
    ...e possible to take the concept of ordered pair as an elementary concept in set theory, but it is more usual to define them in terms of sets. Kuratowksi proposed ...h J. Devlin | authorlink=Keith Devlin | title=Fundamentals of Contemporary Set Theory | series=Universitext | publisher=[[Springer-Verlag]] | year=1979 | isbn=0-
    1 KB (213 words) - 07:01, 21 January 2009
  • Zermelo-Fraenkel axioms
    ...veral possible formulations of [[Set_theory#Axiomatic_set_theory|axiomatic set theory]]. {{cite book |title=Set theory |author=Thomas J Jech |url= http://books.google.com/books?id=pLxq0myANiEC&p
    3 KB (512 words) - 17:28, 2 July 2011
  • Transfinite number
    and initiated the study of infinite numbers, now a major branch of [[set theory]].
    495 bytes (72 words) - 18:31, 20 June 2009
  • Singleton set/Related Articles
    {{r|Set theory}}
    429 bytes (56 words) - 20:24, 11 January 2010
  • Non-Borel set/Bibliography
    | title = Classical descriptive set theory
    292 bytes (32 words) - 03:39, 1 July 2009
  • Complement (disambiguation)
    {{r|Complement (set theory)}}
    296 bytes (31 words) - 11:00, 31 May 2009
  • Fibre (disambiguation)
    {{rpl|Fibre (set theory)}}
    208 bytes (29 words) - 04:09, 26 September 2013
  • Non-Borel set/Advanced
    ...rel; see [[Non-Borel_set/Advanced]] if you are acquainted with descriptive set theory. If you are not, you may find it instructive to try proving that ''A'' is B
    2 KB (402 words) - 20:47, 30 June 2009
  • Caratheodory extension theorem
    ...ins ''X'' itself and is closed under the operation of taking [[complement (set theory)|complement]]s, finite [[union]]s and finite [[intersection]]s in ''X''. Th
    2 KB (324 words) - 16:34, 27 November 2008
  • Kernel of a function
    In [[set theory]], the '''kernel of a function''' is the [[equivalence relation]] on the do
    1 KB (191 words) - 16:00, 7 February 2009
  • Schröder-Bernstein theorem/Related Articles
    {{r|Set theory}}
    207 bytes (28 words) - 18:34, 24 September 2010
  • Element (disambiguation)
    *In [[mathematics]], the term ''element'' is mainly used in [[set theory]], and in various combinations:
    300 bytes (41 words) - 04:19, 2 September 2009
  • Symmetric difference
    In [[set theory]], the '''symmetric difference''' of two sets is the set of elements that b
    676 bytes (121 words) - 10:13, 23 December 2008
  • Algebra/Related Articles
    {{r|Set theory}}
    2 KB (247 words) - 06:00, 7 November 2010
  • Noetherian module
    ...hen considered as a partially [[ordered set]] with respect to [[inclusion (set theory)|inclusion]].
    1 KB (213 words) - 17:17, 7 February 2009
  • Computer science/Related Articles
    {{r|Set theory}}
    3 KB (353 words) - 03:48, 24 September 2013
  • Cartesian product
    * {{cite book | author=Paul Halmos | authorlink=Paul Halmos | title=Naive set theory | series=The University Series in Undergraduate Mathematics | publisher=[[V ...h J. Devlin | authorlink=Keith Devlin | title=Fundamentals of Contemporary Set Theory | series=Universitext | publisher=[[Springer-Verlag]] | year=1979 | isbn=0-
    3 KB (440 words) - 12:26, 30 December 2008
  • Class (disambiguation)
    {{r|Class (set theory)|In mathematics}}
    204 bytes (28 words) - 11:34, 31 May 2009
  • Closed set
    ...closed if <math>X-A=\{x \in X \mid x \notin A\}</math>, the [[complement (set theory)|complement]] of <math>A</math> in <math>X</math>, is an [[open set]]. The
    2 KB (338 words) - 15:26, 6 January 2009
  • Transitive relation
    In [[set theory]], a '''transitive relation''' on a [[set (mathematics)|set]] is a [[relati
    2 KB (295 words) - 14:28, 6 February 2009
  • Absorption (mathematics)
    * In [[set theory]], [[intersection]] and [[union]];
    929 bytes (125 words) - 13:24, 18 November 2022
  • Cantor's diagonal argument/Bibliography
    * {{cite book | author=Paul Halmos | authorlink=Paul Halmos | title=Naive set theory | series=The University Series in Undergraduate Mathematics | publisher=[[V
    408 bytes (50 words) - 12:49, 2 November 2008
  • Intersection/Related Articles
    {{r|Set theory}}
    880 bytes (141 words) - 14:27, 28 November 2008
  • Power set/Related Articles
    {{r|Set theory}}
    881 bytes (141 words) - 14:33, 28 November 2008
  • Georg Cantor
    ...ician '''Georg Ferdinand Ludwig Philipp Cantor''' (1845-1918) introduced [[set theory]] and the concept of [[transfinite number]]s.
    511 bytes (72 words) - 13:06, 16 March 2011
  • Symmetric difference/Related Articles
    {{r|Set theory}}
    898 bytes (142 words) - 10:17, 23 December 2008
  • Schröder-Bernstein property/Related Articles
    {{r|Set theory}}
    969 bytes (152 words) - 13:42, 25 September 2010
  • Disjoint union/Related Articles
    {{r|Set theory}}
    896 bytes (143 words) - 15:56, 28 November 2008
  • Union/Related Articles
    {{r|Set theory}}
    908 bytes (144 words) - 13:34, 12 May 2011
  • Complement (set theory)/Related Articles
    {{r|Set theory}}
    912 bytes (145 words) - 13:30, 28 November 2008
  • Zermelo-Fraenkel axioms/Related Articles
    {{r|Set theory}}
    907 bytes (146 words) - 15:31, 11 May 2011
  • Venn diagram/Related Articles
    {{r|Set theory}}
    910 bytes (145 words) - 14:05, 16 July 2011
  • Boolean algebra/Related Articles
    {{r|Set theory}}
    907 bytes (145 words) - 14:06, 16 July 2011
  • Theory (mathematics)/Related Articles
    {{r|Set theory}}
    980 bytes (151 words) - 14:51, 11 May 2010
  • Pointed set/Related Articles
    {{r|Set theory}}
    271 bytes (43 words) - 12:55, 1 July 2009
  • Standard (mathematics)
    * In [[set theory]], ''standard model'' of the [[natural number]]s usually refers to the set
    1 KB (212 words) - 21:14, 9 September 2020
  • Function (mathematics)/Related Articles
    {{r|Set theory}}
    1 KB (172 words) - 15:25, 15 May 2011
  • Inclusion-exclusion principle/Related Articles
    {{r|Set theory}}
    529 bytes (67 words) - 17:25, 11 January 2010
  • Cardinal number
    In [[set theory]], '''cardinality''' is a property of [[set]]s that generalises the notion ...the [[axiom of foundation]] holds, the set of all sets of minimal [[rank (set theory)|rank]] equinumerous with ''X'' can be used. If the [[axiom of choice]] is
    11 KB (1,808 words) - 17:50, 26 June 2009
  • Inclusion-exclusion principle
    The '''inclusion-exclusion principle''' is a [[theorem]] of [[set theory]] relating to the [[cardinality]] of a set defined as the [[union (mathemat
    1 KB (237 words) - 19:41, 7 April 2009
  • Equivalence relation/Bibliography
    * {{cite book | author=Paul Halmos | authorlink=Paul Halmos | title=Naive set theory | series=The University Series in Undergraduate Mathematics | publisher=[[V
    579 bytes (73 words) - 02:31, 13 December 2008
  • Noetherian ring
    ...hen considered as a partially [[ordered set]] with respect to [[inclusion (set theory)|inclusion]].
    2 KB (326 words) - 09:55, 23 December 2008
  • Axiom of choice/Bibliography
    * {{cite book | author=Paul Halmos | authorlink=Paul Halmos | title=Naive set theory | series=The University Series in Undergraduate Mathematics | publisher=[[V
    620 bytes (76 words) - 13:07, 5 January 2013
  • Distributivity
    ** In [[set theory]], [[intersection]] distributes over [[union]] and union distributes over i
    2 KB (226 words) - 13:15, 18 November 2022
  • Union/Bibliography
    * {{cite book | author=Paul Halmos | authorlink=Paul Halmos | title=Naive set theory | series=The University Series in Undergraduate Mathematics | publisher=[[V
    705 bytes (92 words) - 14:12, 23 November 2008
  • Relation composition
    In [[set theory]], '''composition''' is an operation on [[relation (mathematics)|relations]
    642 bytes (110 words) - 17:40, 6 February 2009
  • Fuzzy subalgebra
    * Zimmermann H., ''Fuzzy Set Theory and its Applications'' (2001), ISBN 978-0-7923-7435-0. * Klir G. , UTE H. St.Clair and Bo Yuan ''Fuzzy Set Theory Foundations and Applications'',1997.
    4 KB (725 words) - 01:25, 12 December 2008
  • Fuzzy subset
    ...properties as ''"to be small"'', ''"to be close to 6"'' and so on. Now, in set theory given a set ''S'' and a "well defined" property ''P'', the ''axiom of comp ...erent empty subsets and therefore there is not a unique empty subset as in set theory.
    6 KB (993 words) - 08:55, 30 May 2009
  • Characteristic function/Related Articles
    {{r|Set theory}}
    844 bytes (136 words) - 13:26, 8 December 2008
  • Filter (mathematics)/Related Articles
    {{r|Set theory}}
    864 bytes (138 words) - 17:27, 27 November 2008
  • Cartesian product/Related Articles
    {{r|Set theory}}
    927 bytes (149 words) - 02:35, 3 November 2008
  • Continuum hypothesis/Bibliography
    ...m of choice and of the generalized continuum-hypothesis with the axioms of set theory'') Paul J. Cohen, ''Set theory and the continuum hypothesis''. New York, Amsterdam. 1966.
    4 KB (568 words) - 15:50, 14 July 2009
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