---
tag: MSXX2P86CY
kind: concept
name: Arity
msc: [08A02, 03C07]
sources:
  - url: https://en.wikipedia.org/wiki/Arity
same_as:
  wikidata: Q1315869
  wikipedia: Arity
---

## Summary

The arity of an operation, a function or a relation is the number of arguments it takes.
An operation of arity $n$ is called $n$-ary: nullary for $0$, unary for $1$, binary for $2$ and ternary for $3$.
Arities are part of every [[signature|WDVVEYD6AT]], and they tell what kind of interpretation each symbol gets in a [[structure|983GZBQYT4]].

## Explanations

### L1 human

The arity counts the inputs.
Negation $x \mapsto -x$ takes one number, so its arity is $1$.
Addition $(x, y) \mapsto x + y$ takes two numbers, so its arity is $2$.
The relation "$x$ lies between $y$ and $z$" compares three points, so its arity is $3$.
A constant such as $0$ takes no input at all and is seen as an operation of arity $0$.