Unary operation

Remarks

Example: the absolute value $x \mapsto \abs{x}$ is a unary operation on $\R$, because $\abs{x} \in \R$ for every $x \in \R$.

Non-example: the map $x \mapsto 1/x$ is not a unary operation on $\R$, because it is not defined at $0$. It is a unary operation on $\R \setminus \set{0}$.

A unary operation is often written in prefix notation $f(x)$ or $-x$, in postfix notation $x^{-1}$ or $x!$, or with a bar $\bar{x}$. Here $A^1$ is identified with $A$.