identity element

< Earlier form of the word in English was idemptitie (1560s), from Medieval Latin idemptitas. Term identity crisis first recorded 1954. Identity theft attested from 1995.

n.

1. The set of behavioral or personal characteristics by which an individual is recognizable as a member of a group.
2. The distinct personality of an individual regarded as a persisting entity; individuality.

1. The element of a set of numbers that when combined with another number under a particular binary operation leaves the second number unchanged. For example, 0 is the identity element under addition for the real numbers, since for any real number a, a + 0 = a, and 1 is the identity element under multiplication for the real numbers, since a X 1 = a.