Binary operation

From Citizendium
Revision as of 22:07, 7 November 2008 by Richard Pinch (Talk | contribs) (new entry, just a stub)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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: