# Today I Learned

Some of the things I've learned every day since Oct 10, 2016

## 55: Idempotent Unary Operators

A unary operator $f$ is idempotent if and only if

$f(x) = f^n(x)$

for all $x$ and all $n \geq 1$. That is, the result of calling the operator once on an element is the same as that of calling it any positive number of times on that element. This means that it maps each element of the underlying set to an $f$-invariant element of that set.

Examples of idempotent unary operators include the absolute value function, the identity function, and the zero tranformation.