identity

(ī-dĕnˈtĭ-tē)

1. The collective aspect of the set of characteristics by which a thing is definitively recognizable or known: “If the broadcast group is the financial guts of the company, the news division is its public identity” (Bill Powell).
2. The set of behavioral or personal characteristics by which an individual is recognizable as a member of a group.
3. The quality or condition of being the same as something else.
4. The distinct personality of an individual regarded as a persisting entity; individuality.
5. Information, such as an identification number, used to establish or prove a person's individuality, as in providing access to a credit account.
6. Mathematics
   a. An equation that is satisfied by any number that replaces the letter for which the equation is defined.
   b. Identity element.