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{{r|Set theory}}

A classic theorem of set theory asserting that sets can be ordered by size.

...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

In [[set theory]], a '''subset''' of a [[set (mathematics)|set]] ''X'' is a set ''A'' whose

...veral possible formulations of [[Set_theory#Axiomatic_set_theory|axiomatic set theory]].

In [[set theory]], the '''characteristic function''' or '''indicator function''' of a [[sub

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:

...ages}}</noinclude>(1845-1918) Danish-German mathematician who introduced [[set theory]] and the concept of [[transcendental number]]s

...open set]]s are those which have [[countable set|countable]] [[complement (set theory)|complement]], together with the empty set. Equivalently, the [[closed set

...the [[open set]]s are those which have [[finite set|finite]] [[complement (set theory)|complement]], together with the empty set. Equivalently, the [[closed set

In [[set theory]], a '''pointed set''' is a [[set (mathematics)|set]] together with a disti

...ties that have the same structure as the [[Schröder-Bernstein theorem]] of set theory.

{{r|Set theory}} {{r|Complement (set theory)}}

{{r|descriptive set theory}}

* {{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-

...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

...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

...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

...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

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