Editing Subset (section)

==⊂ and ⊃ symbols==
Some authors use the symbols <math>\subset</math> and <math>\supset</math> to indicate {{em|subset}} and {{em|superset}} respectively; that is, with the same meaning as and instead of the symbols <math>\subseteq</math> and <math>\supseteq.</math><ref>{{Citation|last1=Rudin|first1=Walter|author1-link=Walter Rudin|title=Real and complex analysis|publisher=[[McGraw-Hill]]|location=New York|edition=3rd|isbn=978-0-07-054234-1|mr=924157 |year=1987|page=6}}</ref> For example, for these authors, it is true of every set ''A'' that <math>A \subset A.</math> (a [[reflexive relation]]).

Other authors prefer to use the symbols <math>\subset</math> and <math>\supset</math> to indicate {{em|proper}} (also called strict) subset and {{em|proper}} superset respectively; that is, with the same meaning as and instead of the symbols <math>\subsetneq</math> and <math>\supsetneq.</math><ref>{{Citation|title=Subsets and Proper Subsets|url=http://it.edgecombe.edu/homepage/killorant/MAT140/Module1/Subsets.pdf|access-date=2012-09-07|archive-url=https://web.archive.org/web/20130123202559/http://it.edgecombe.edu/homepage/killorant/MAT140/Module1/Subsets.pdf|archive-date=2013-01-23|url-status=dead }}</ref> This usage makes <math>\subseteq</math> and <math>\subset</math> analogous to the [[inequality (mathematics)|inequality]] symbols <math>\leq</math> and <math><.</math> For example, if <math>x \leq y,</math> then ''x'' may or may not equal ''y'', but if <math>x < y,</math> then ''x'' definitely does not equal ''y'', and ''is'' less than ''y'' (an [[irreflexive relation]]). Similarly, using the convention that <math>\subset</math> is proper subset, if <math>A \subseteq B,</math> then ''A'' may or may not equal ''B'', but if <math>A \subset B,</math> then ''A'' definitely does not equal ''B''.