identity element

from The American Heritage® Dictionary of the English Language, 5th Edition.

• 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.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun 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

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• noun an operator that leaves unchanged the element on which it operates