---
tag: W7NFRDY0GA
kind: definition
name: Unary operation
msc: [08A02, 08A62]
defines: Q2W26ZY10B
uses: [EJ8YJVM9BW, 0EPAT51DXQ]
sources:
  - url: https://en.wikipedia.org/wiki/Unary_operation
---

## Definition

Let $A$ be a set.
A *unary operation* on $A$ is a [[finitary operation|EJ8YJVM9BW]] of arity $1$, that is, a [[function|0EPAT51DXQ]] $f \colon A \to A$.

## 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 $A$.