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# binary operation

A *binary operation* on a set $X$ is a function from the Cartesian product $X\times X$ to $X$. A binary operation is sometimes called *internal composition*.

Rather than using function notation, it is usual to write binary operations with an operation symbol between elements, or even with no operation at all, it being understood that juxtaposed elements are to be combined using an operation that should be clear from the context.

Thus, addition of real numbers is the operation

$(x,y)\mapsto x+y,$ |

and multiplication in a groupoid is the operation

$(x,y)\mapsto xy.$ |

Related:

Arity, Operation

Synonym:

internal composition

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

08A99*no label found*

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