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- ...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
- 20 bytes (2 words) - 12:20, 30 November 2008
- 34 bytes (5 words) - 12:47, 13 December 2008
- 19 bytes (2 words) - 13:25, 23 November 2008
- 135 bytes (15 words) - 06:12, 22 October 2013
- 26 bytes (2 words) - 14:14, 23 November 2008
- Paul R. Halmos, ''Naive Set Theory.'' <br> ''A detailed informal introduction based on ZF set theory.''743 bytes (103 words) - 10:26, 10 July 2011
- 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 re805 bytes (135 words) - 13:24, 28 November 2008
- 710 bytes (65 words) - 15:53, 30 May 2010
- 94 bytes (12 words) - 12:32, 30 November 2008
- 127 bytes (21 words) - 13:07, 13 December 2008
- {{r|Naive set theory}} {{r|Axiomatic set theory}}477 bytes (65 words) - 07:22, 22 July 2011
- 139 bytes (22 words) - 13:28, 28 November 2008
- ...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
- *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=Stanf865 bytes (130 words) - 09:37, 4 July 2011
- {{r|Set theory}}912 bytes (145 words) - 13:30, 28 November 2008
Page text matches
- Paul R. Halmos, ''Naive Set Theory.'' <br> ''A detailed informal introduction based on ZF set theory.''743 bytes (103 words) - 10:26, 10 July 2011
- 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
- In set theory, this is a set without elements, usually denoted <math>\{~\}</math> or <mat184 bytes (29 words) - 01:06, 19 February 2009
- A [[set theory|set]] with an [[order relation]]83 bytes (11 words) - 10:23, 15 July 2011
- {{r|Set theory}}370 bytes (47 words) - 17:50, 26 June 2009
- Set theory assertion that if S is a set of disjoint, non-empty sets, then there exists182 bytes (30 words) - 08:45, 27 November 2011
- {{r|set theory}} {{r|history of set theory}}206 bytes (26 words) - 16:28, 11 June 2009
- {{r|Naive set theory}} {{r|Axiomatic set theory}}477 bytes (65 words) - 07:22, 22 July 2011
- In [[set theory]], a '''singleton''' is a [[set (mathematics)|set]] with exactly one elemen199 bytes (28 words) - 12:58, 7 February 2009
- ...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.goo764 bytes (113 words) - 09:14, 16 May 2011
- 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 re805 bytes (135 words) - 13:24, 28 November 2008
- {{r|Class (set theory)|Class}}648 bytes (83 words) - 10:12, 11 May 2009
- {{r|Set theory}} {{r|Naive set theory}}507 bytes (65 words) - 07:17, 22 July 2011
- A chapter of fuzzy set theory.67 bytes (9 words) - 08:05, 4 September 2009
- *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=Stanf865 bytes (130 words) - 09:37, 4 July 2011
- *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=Stanf865 bytes (130 words) - 17:17, 2 July 2011
- # 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
- {{r|Set theory}}245 bytes (29 words) - 09:38, 18 June 2009
- 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''' is the main success of fuzzy set theory and it is devoted to useful applications.472 bytes (59 words) - 23:34, 14 February 2010
- {{r|Set theory}}307 bytes (44 words) - 16:27, 26 July 2008
- A classic theorem of set theory asserting that sets can be ordered by size.111 bytes (17 words) - 17:30, 24 September 2010
- ...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=[[V1 KB (146 words) - 17:50, 26 June 2009
- In [[set theory]], a '''subset''' of a [[set (mathematics)|set]] ''X'' is a set ''A'' whose596 bytes (101 words) - 12:42, 30 December 2008
- ...veral possible formulations of [[Set_theory#Axiomatic_set_theory|axiomatic set theory]].132 bytes (17 words) - 15:22, 11 May 2011
- In [[set theory]], the '''characteristic function''' or '''indicator function''' of a [[sub2 KB (242 words) - 02:01, 2 February 2009
- 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
- ...ages}}</noinclude>(1845-1918) Danish-German mathematician who introduced [[set theory]] and the concept of [[transcendental number]]s150 bytes (17 words) - 13:07, 16 March 2011
- ...open set]]s are those which have [[countable set|countable]] [[complement (set theory)|complement]], together with the empty set. Equivalently, the [[closed set1,004 bytes (134 words) - 22:48, 17 February 2009
- ...the [[open set]]s are those which have [[finite set|finite]] [[complement (set theory)|complement]], together with the empty set. Equivalently, the [[closed set1,007 bytes (137 words) - 22:52, 17 February 2009
- In [[set theory]], a '''pointed set''' is a [[set (mathematics)|set]] together with a disti1 KB (168 words) - 12:06, 22 November 2008
- ...ties that have the same structure as the [[Schröder-Bernstein theorem]] of set theory.166 bytes (23 words) - 18:06, 25 September 2010
- {{r|Set theory}} {{r|Complement (set theory)}}914 bytes (146 words) - 13:36, 28 November 2008
- {{r|descriptive set theory}}217 bytes (31 words) - 10:31, 21 June 2009
- * {{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
- ...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=[[V611 bytes (74 words) - 12:55, 30 November 2008
- ...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=[[V1 KB (135 words) - 16:24, 4 January 2009
- ...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=[[V649 bytes (78 words) - 17:27, 3 November 2008
- ...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=[[V649 bytes (78 words) - 17:30, 3 November 2008
- 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=[[V2 KB (284 words) - 14:24, 28 November 2008
- 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
- requires advanced results from [[descriptive set theory]].2 KB (252 words) - 11:44, 2 December 2010
- 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=[[V2 KB (264 words) - 17:13, 4 November 2008
- ...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=[[V774 bytes (96 words) - 02:14, 11 November 2008
- 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
- {{r|Inclusion (set theory)}}108 bytes (14 words) - 11:04, 31 May 2009
- {{r|Set theory}}267 bytes (32 words) - 19:16, 17 June 2009
- ...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
- ...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
- ...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&p3 KB (512 words) - 17:28, 2 July 2011
- and initiated the study of infinite numbers, now a major branch of [[set theory]].495 bytes (72 words) - 18:31, 20 June 2009
- {{r|Set theory}}429 bytes (56 words) - 20:24, 11 January 2010
- | title = Classical descriptive set theory292 bytes (32 words) - 03:39, 1 July 2009
- {{r|Complement (set theory)}}296 bytes (31 words) - 11:00, 31 May 2009
- {{rpl|Fibre (set theory)}}208 bytes (29 words) - 04:09, 26 September 2013
- ...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 B2 KB (402 words) - 20:47, 30 June 2009
- ...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''. Th2 KB (324 words) - 16:34, 27 November 2008
- In [[set theory]], the '''kernel of a function''' is the [[equivalence relation]] on the do1 KB (191 words) - 16:00, 7 February 2009
- {{r|Set theory}}207 bytes (28 words) - 18:34, 24 September 2010
- *In [[mathematics]], the term ''element'' is mainly used in [[set theory]], and in various combinations:300 bytes (41 words) - 04:19, 2 September 2009
- In [[set theory]], the '''symmetric difference''' of two sets is the set of elements that b676 bytes (121 words) - 10:13, 23 December 2008
- {{r|Set theory}}2 KB (247 words) - 06:00, 7 November 2010
- ...hen considered as a partially [[ordered set]] with respect to [[inclusion (set theory)|inclusion]].1 KB (213 words) - 17:17, 7 February 2009
- {{r|Set theory}}3 KB (353 words) - 03:48, 24 September 2013
- * {{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
- {{r|Class (set theory)|In mathematics}}204 bytes (28 words) - 11:34, 31 May 2009
- ...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]]. The2 KB (338 words) - 15:26, 6 January 2009
- In [[set theory]], a '''transitive relation''' on a [[set (mathematics)|set]] is a [[relati2 KB (295 words) - 14:28, 6 February 2009
- * In [[set theory]], [[intersection]] and [[union]];929 bytes (125 words) - 13:24, 18 November 2022
- * {{cite book | author=Paul Halmos | authorlink=Paul Halmos | title=Naive set theory | series=The University Series in Undergraduate Mathematics | publisher=[[V408 bytes (50 words) - 12:49, 2 November 2008
- {{r|Set theory}}881 bytes (141 words) - 14:33, 28 November 2008
- {{r|Set theory}}880 bytes (141 words) - 14:27, 28 November 2008
- ...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
- {{r|Set theory}}898 bytes (142 words) - 10:17, 23 December 2008
- {{r|Set theory}}969 bytes (152 words) - 13:42, 25 September 2010
- {{r|Set theory}}896 bytes (143 words) - 15:56, 28 November 2008
- {{r|Set theory}}908 bytes (144 words) - 13:34, 12 May 2011
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- {{r|Set theory}}980 bytes (151 words) - 14:51, 11 May 2010
- {{r|Set theory}}271 bytes (43 words) - 12:55, 1 July 2009
- * In [[set theory]], ''standard model'' of the [[natural number]]s usually refers to the set1 KB (212 words) - 21:14, 9 September 2020
- {{r|Set theory}}1 KB (172 words) - 15:25, 15 May 2011
- {{r|Set theory}}529 bytes (67 words) - 17:25, 11 January 2010
- 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]] is11 KB (1,808 words) - 17:50, 26 June 2009
- The '''inclusion-exclusion principle''' is a [[theorem]] of [[set theory]] relating to the [[cardinality]] of a set defined as the [[union (mathemat1 KB (237 words) - 19:41, 7 April 2009
- * {{cite book | author=Paul Halmos | authorlink=Paul Halmos | title=Naive set theory | series=The University Series in Undergraduate Mathematics | publisher=[[V579 bytes (73 words) - 02:31, 13 December 2008
- ...hen considered as a partially [[ordered set]] with respect to [[inclusion (set theory)|inclusion]].2 KB (326 words) - 09:55, 23 December 2008
- * {{cite book | author=Paul Halmos | authorlink=Paul Halmos | title=Naive set theory | series=The University Series in Undergraduate Mathematics | publisher=[[V620 bytes (76 words) - 13:07, 5 January 2013
- ** In [[set theory]], [[intersection]] distributes over [[union]] and union distributes over i2 KB (226 words) - 13:15, 18 November 2022
- * {{cite book | author=Paul Halmos | authorlink=Paul Halmos | title=Naive set theory | series=The University Series in Undergraduate Mathematics | publisher=[[V705 bytes (92 words) - 14:12, 23 November 2008
- In [[set theory]], '''composition''' is an operation on [[relation (mathematics)|relations]642 bytes (110 words) - 17:40, 6 February 2009
- * 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
- ...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
- {{r|Set theory}}844 bytes (136 words) - 13:26, 8 December 2008
- {{r|Set theory}}864 bytes (138 words) - 17:27, 27 November 2008
- {{r|Set theory}}927 bytes (149 words) - 02:35, 3 November 2008
- ...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
- ...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
- ...e notion of comparison between [[number]]s and magnitudes, or [[inclusion (set theory)|inclusion]] between sets or [[algebraic structure]]s. ...maximal within the family of chains ordered by set-theoretic [[inclusion (set theory)|inclusion]]).11 KB (1,918 words) - 18:23, 17 January 2010
- ...lved.) The very existence of various sets introduced below is addressed by set theory, for example by the [[Zermelo-Fraenkel axioms]].<ref name=Jech/> See {{cite book |title=Naive set theory |author=Paul Richard Halmos |chapter=Section 9: Families |url=http://books.17 KB (2,828 words) - 10:37, 24 July 2011
- ...mes '''Cantor-Schröder-Bernstein theorem''') is a fundamental theorem of [[set theory]]. * '''1895''' [[Georg Cantor]] states the theorem in his first paper on set theory and transfinite numbers (as an easy consequence of the linear order of card8 KB (1,275 words) - 15:34, 23 September 2013
- ...mes '''Cantor-Schröder-Bernstein theorem''') is a fundamental theorem of [[set theory]]. * '''1895''' [[Georg Cantor]] states the theorem in his first paper on set theory and transfinite numbers (as an easy consequence of the linear order of card8 KB (1,281 words) - 15:39, 23 September 2013
- ...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
- who showed that – in set theory including the [[axiom of choice]] – ...othesis is independent of the usual [[axiomatic set theory|(ZFC) axioms of set theory]].8 KB (1,289 words) - 20:20, 15 July 2009
- ...e subjects. For example, arithmetic has the product of a pair of numbers, set theory has the Cartesian product of a pair of sets and logic has the conjunction o7 KB (1,151 words) - 14:44, 26 December 2013
- ...b> is a subset of ''E''<sub>''n''+1</sub> for all ''n'', then the [[Union (set theory)|union]] of the sets ''E''<sub>''n''</sub> is measurable, and ...a subset of ''E''<sub>''n''</sub> for all ''n'', then the [[Intersection (set theory)|intersection]] of the sets ''E''<sub>''n''</sub> is measurable; furthermor14 KB (2,350 words) - 17:37, 10 November 2007
- ...s [[nitrogen]]", and unlike other explanations - realist or nominalist - [[set theory]] provides a mature understanding of classes including identity conditions.5 KB (829 words) - 01:53, 15 January 2010
- ...ann Benedict Listing]]. Modern topology depends strongly on the ideas of [[set theory]], developed by [[Georg Cantor]] in the later part of the 19th century. [[H1 KB (206 words) - 14:09, 29 December 2008
- or, in set theory, as a specific set that serves as a concrete object (model) In modern mathematics, in particular because of set theory and16 KB (2,562 words) - 00:45, 13 October 2009
- * Zimmermann H., ''Fuzzy Set Theory and its Applications'' (2001), ISBN 0-7923-7435-5.3 KB (382 words) - 05:55, 10 September 2009
- In the set theory, infinity appears directly; for instance,18 KB (2,797 words) - 14:37, 30 January 2011
- the sum being taken on ''E''<sub>1</sub> of the ''d'' points on the [[fibre (set theory)|fibre]] over ''Q''. This is indeed an isogeny, and the [[function composi4 KB (647 words) - 15:51, 7 February 2009
- ...alogy to the [[Schröder-Bernstein theorem|theorem]] of the same name (from set theory).6 KB (944 words) - 15:09, 23 September 2013
- ...alogy to the [[Schröder-Bernstein theorem|theorem]] of the same name (from set theory).6 KB (944 words) - 08:32, 14 October 2013
- ...defined object that underlies some [[Set_theory#The_paradoxes|paradoxes in set theory]]. The idea of a universe ''U'' need not be paradoxical, however, if one co11 KB (1,760 words) - 09:20, 15 June 2012
- ...Octonion]]s were discovered in 1843. [[Georg Cantor]], through its naive [[set theory]], formally defined the notion of [[infinity]] in 1895. [[Kurt Hensel]] fir11 KB (1,701 words) - 20:07, 1 July 2021
- ...>, we define the ''closed sets'' of <math>X</math> to be the [[complement (set theory)|complement]]s (in <math>X</math>) of the open sets; the closed sets of <ma15 KB (2,586 words) - 16:07, 4 January 2013
- ==Functions in set theory== In [[set theory]], functions are regarded as a special class of [[relation (mathematics)|re15 KB (2,342 words) - 06:26, 30 November 2011
- * Zimmermann H., ''Fuzzy Set Theory and its Applications'' (2001), ISBN 0-7923-7435-5.10 KB (1,611 words) - 22:55, 20 February 2010
- ...for α. For example, let ʘ be the minimum, ''T'' be a system of axioms for set theory such that the choice axiom ''CA'' does not depend on ''T''. Then we can co Then, despite the fact that no vague predicate is considered in set theory, in the metalanguage we can consider a vague meta-predicate as "is acceptab23 KB (3,576 words) - 16:38, 29 January 2017
- ...p]]s that are the group of integers [[modular arithmetic|modulo]] ''n''. [[Set theory]] is a branch of [[logic]] and not technically a branch of algebra.18 KB (2,669 words) - 08:38, 17 April 2024
- ...gical independence|independent]] from the [[axiomatic set theory|axioms of set theory]].19 KB (2,948 words) - 10:07, 28 February 2024
- ...one may use untyped variables and express everything in the framework of [[set theory]] by means of guarded quantification. In this case maps and sets are reduce ...ld have to pay me money to make me twist my brain around HOL and its typed set theory.21 KB (3,291 words) - 16:07, 3 November 2013
- ...mportant work (equally significant, but less well known) was his work in [[set theory]], where he proved that [[Georg Cantor]]'s puzzling [[Continuum Hypothesis]3 KB (375 words) - 15:26, 11 May 2011
- ...n of mathematics]]. Also [[category theory]] pretends to the throne of the set theory.<ref>{{harvnb|Lawvere|Rosebrugh|2003}}.</ref> ...ed in mathematics two centuries later, especially, as a formal language of set theory. In the form introduced by Bourbaki this language contains four logical sig34 KB (5,174 words) - 21:32, 25 October 2013
- One of Russell's primary contributions in philosophy, mathematics and [[set theory]] is [[Russell's Paradox]], which he discovered in 1901. The paradox is tha12 KB (1,964 words) - 11:47, 2 February 2023
- ...ncient to modern times, Volume 3 |chapter=Chapter 51: §2: The paradoxes of set theory |url=http://books.google.com/books?id=8YaBuGcmLb0C&pg=PA1183 |author=Morris ...ncient to modern times, Volume 3 |chapter=Chapter 51: §2: The paradoxes of set theory |url=http://books.google.com/books?id=8YaBuGcmLb0C&pg=PA1183 |author=Morris9 KB (1,587 words) - 23:56, 16 May 2011
- ...t every mathematical statement or proof could be cast into formulas within set theory. ...eart of mathematics to other fields: to [[Mathematical logic|logic]], to [[set theory]] ([[Foundations of mathematics|foundations]]), to the empirical mathematic30 KB (4,289 words) - 16:03, 20 January 2023
- Hash tables are often used to implement dictionaries or [[set theory|sets]]. Internet [[router|routers]] usually use a hash table to correlate5 KB (832 words) - 13:00, 16 January 2008
- ...allowed the formalisation of mathematics, and drove the investigation of [[set theory]], allowed the development of [[Alfred Tarski]]'s approach to [[model theor ...tical logic, they have been but two of the four pillars of the subject. [[Set theory]] originated in the study of the infinite by [[Georg Cantor]], and it has b32 KB (4,979 words) - 21:47, 12 November 2011
- ...at the [[continuum hypothesis]] is consistent with the axioms of classical set theory. He was interested in the mathematical aspects of the [[theory of relativit30 KB (4,343 words) - 13:59, 18 February 2024
- ...ch class set'' is a collection of three or more pitches, and ''pitch class set theory'' studies characteristics of differently chosen sets. The idea is to genera ...e functionally the same, one octave apart). Among the conventions of music set theory are:<ref name=Mayfield/>32 KB (5,025 words) - 10:07, 28 February 2024
- ...y other forms. [[Musical set theory]] is the application of mathematical [[set theory]] to music, first applied to [[atonal music]]. [[Speculative music theory]]30 KB (4,645 words) - 20:32, 19 July 2013
- ...tribute tables of both inputs into a single new output. An [[intersection (set theory)|intersect]] overlay defines the area where both inputs overlap and retains41 KB (6,343 words) - 17:02, 22 March 2024
- ::: —Alec Rogers: ''Cognitive Set Theory, p. 85'' {{cite book |author=Alec Rogers |title=Cognitive Set Theory |url=http://books.google.com/books?id=qkEqfI3H4zkC&pg=PA85 |pages=p. 85 |ch82 KB (12,424 words) - 15:58, 2 August 2016
- ...universes ultimately contains the other."</font> –Alec Rogers: ''Cognitive Set Theory'', p.85<ref name=Rogers/> {{cite book |author=Alec Rogers |title=Cognitive Set Theory |url=http://books.google.com/books?id=qkEqfI3H4zkC&pg=PA85 |page=85 |chapte93 KB (14,229 words) - 19:42, 6 February 2016