# identity element

identity element
noun

The definition of an identity element is a number that combines with other elements in a mathematical equation but does not change them.

An example of an identity element is 0 in the equation 5+0=5.

## identity element

an element of a mathematical system that does not change the other elements in the system when it operates on them: zero is the identity element for addition (x + 0 = x) and one is the identity element for multiplication (y × 1 = y)

## identity element

noun

The element of a set of numbers that when combined with another number in a particular operation leaves that number unchanged. For example, 0 is the identity element under addition for the real numbers, since if

*a*is any real number,*a*+ 0 = 0 +*a*=*a.*Similarly, 1 is the identity element under multiplication for the real numbers, since*a*× 1 = 1 ×*a*=*a.*Also called*unity*.## identity-element

Noun

(*plural* identity elements)

- (algebra) A member of a structure which, when applied to any other element via a binary operation, induces an identity mapping; more specifically, given an operation
***, an element*I*is- a
*left identity*if*I * x = x*for any*x*in the structure - a
*right identity*,*x * I = x*for any*x*in the structure - simply an
*identity element*if both are true

- a