---
tag: Q2W26ZY10B
kind: concept
name: Unary operation
msc: [08A02, 08A62]
specializes: [EJ8YJVM9BW]
sources:
  - url: https://en.wikipedia.org/wiki/Unary_operation
same_as:
  wikidata: Q657596
  wikipedia: Unary operation
---

## Summary

A unary operation on a set $A$ is a [[finitary operation|EJ8YJVM9BW]] of [[arity|MSXX2P86CY]] $1$, that is, a function from $A$ to $A$.
Negation of numbers, the inverse in a [[group|G5S1M9]] and the complement of a set are unary operations.
An algebra whose operations are all unary is a [[unary algebra|XD10P9CJMD]].

## Explanations

### L1 human

A unary operation takes one element and gives back one element of the same set.
On the integers, $x \mapsto -x$ and $x \mapsto x + 1$ are unary operations.
On the subsets of a fixed set $X$, taking the complement $Y \mapsto X \setminus Y$ is a unary operation.
The square root is not a unary operation on the real numbers, because $\sqrt{-1}$ is not a real number.