Identity function: Difference between revisions
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In [[mathematics]], the '''identity function''' on a set ''X'' is the [[function (mathematics)|function]] from ''X'' to itself which maps each element to itself: | In [[mathematics]], the '''identity function''' on a set ''X'' is the [[function (mathematics)|function]] from ''X'' to itself which maps each element to itself: | ||
:<math>\mbox{id}_X : x \mapsto x .\,</math> | :<math>\mbox{id}_X : x \mapsto x .\,</math> | ||
The identity function is [[invertible function|invertible]] (and is its own [[inverse function]]). It is a [[permutation]] of the set, and is the [[identity element]] of the [[symmetric group]] on ''X''. | The identity function is [[invertible function|invertible]] (and is its own [[inverse function]]). It is a [[permutation]] of the set, and is the [[identity element]] of the [[symmetric group]] on ''X''.[[Category:Suggestion Bot Tag]] | ||
Latest revision as of 07:01, 31 August 2024
In mathematics, the identity function on a set X is the function from X to itself which maps each element to itself:
The identity function is invertible (and is its own inverse function). It is a permutation of the set, and is the identity element of the symmetric group on X.