= Identity function
{title2=$\operatorname{id}$}
{wiki}
= Identity map
{synonym}
The <identity function> on a <set> $X$ maps each $x\in X$ to itself: $\operatorname{id}_X(x)=x$. It changes no information. For every <function> $f:X\to Y$, <function composition> satisfies $f\circ\operatorname{id}_X=f$ and $\operatorname{id}_Y\circ f=f$. The subscripts specify the appropriate source or target <set>. An <inverse function> reverses a <bijection> exactly when the two possible compositions are these <identity functions>.
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