identity elementidentity element
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.
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)
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 .
(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