Difference between revisions of "Binary operation"

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In [[mathematics]], a '''binary operation''' on a set is a function of two variables which assigns a value to any pair of elements of the set: principal motivating examples include the [[arithmetic]] and [[elementary algebra]]ic operations of addition, subtraction, multiplication and division.
 
In [[mathematics]], a '''binary operation''' on a set is a function of two variables which assigns a value to any pair of elements of the set: principal motivating examples include the [[arithmetic]] and [[elementary algebra]]ic operations of addition, subtraction, multiplication and division.
  

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In mathematics, a binary operation on a set is a function of two variables which assigns a value to any pair of elements of the set: principal motivating examples include the arithmetic and elementary algebraic operations of addition, subtraction, multiplication and division.

Formally, a binary operation on a set S is a function on the Cartesian product

given by

using operator notation rather than functional notation, which would call for writing .

Properties

A binary operation may satisfy further conditions.

Special elements which may be associated with a binary operations include: