empty set

An is a set $\emptyset$ that contains no elements. The Zermelo-Fraenkel Axioms of set theory imply that there exists an empty set. One constructs an empty set by starting with any set $X$ and then applying the axiom of separation to form the empty set $\emptyset:=\{x\in X\mid x\neq x\}$.

An empty set is a subset of every other set, and any two empty sets are equal. Alternative notations for the empty set include $\{\}$ and $\varnothing$.

Title empty set EmptySet 2013-03-22 11:49:55 2013-03-22 11:49:55 djao (24) djao (24) 8 djao (24) Definition msc 03-00 msc 65H05 msc 65H10 null set