Operation (Mathematics)

Operation

An operation is a special type of function defined on a set $S$ that takes one or more elements of $S$ and produces another element of $S$.

Formally, an $n$-ary operation is a function $f:S^n\to S$ where $n\ge 1$ is the number of inputs.

Key connections:

• domain/codomain: The domain is $S^n$, codomain is $S$.
• image: The outputs of an operation are a subset of $S$.
• Closure Property: A set $S$ is closed under an operation if all outputs of the operation are in $S$.