Idempotent function
= Idempotent function
{title2=$f\circ f=f$}
= Idempotent map
{synonym}
A <self-map> $f:X\to X$ is idempotent if its <function composition> with itself leaves it unchanged: $f(f(x))=f(x)$ for every $x$. Equivalently, every element of its <image of a function> is a <fixed point>. For example, the <function> on $\{a,b,c\}$ sending $a$ to $b$, $b$ to $b$, and $c$ to $c$ is idempotent. A second application makes no further change.