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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>.

requires advanced results from [[descriptive set theory]].

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

...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

A characteristic property of finite sets (which, in [[set theory]] is used to ''define'' finite sets) is the following:

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...s and [[Kurt Gödel]] showed that it was independent of the other axioms of set theory.

...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-

...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

and initiated the study of infinite numbers, now a major branch of [[set theory]].

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| title = Classical descriptive set theory

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{{rpl|Fibre (set theory)}}

...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

...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

In [[set theory]], the '''kernel of a function''' is the [[equivalence relation]] on the do

{{r|Set theory}}

*In [[mathematics]], the term ''element'' is mainly used in [[set theory]], and in various combinations: