Binary operation
From Citizendium, the Citizens' Compendium
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 operation include:
- Neutral element I:
for all x
- Absorbing element O:
for all x
- Idempotent element E:
