Idempotent function ($f\circ f=f$)

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.