identity

American Heritage® Dictionary of the English Language, Fourth Edition

1. n. 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. n. The set of behavioral or personal characteristics by which an individual is recognizable as a member of a group.
3. n. The quality or condition of being the same as something else.
4. n. The distinct personality of an individual regarded as a persisting entity; individuality.
5. n. Information, such as an identification number, used to establish or prove a person's individuality, as in providing access to a credit account.
6. n. Mathematics An equation that is satisfied by any number that replaces the letter for which the equation is defined.
7. n. Mathematics Identity element.

Century Dictionary and Cyclopedia

1. n. The state of being the same; absolute sameness; that relation which anything bears to itself; loosely, essential or practical sameness. Properly, identity belongs only to the individual, thing, being, event, etc.
2. n. In mathematics: The relation of an expression to another symbol for itself: often denoted by three short parallel horizontal lines, ≡ (derived from the mark of equality, =).
3. n. In algebra: A relation of equivalence dependent only upon the very nature of the operations involved, and not at all upon the particular numbers operated with: for example, the identity of ab with ba.
4. n. An identical equation; an equation for any letter in which any number whatsoever may be substituted without destroying the equality or restricting the values of any other letter: for example, (a + b) + c = a + (b + c).

Wiktionary

1. n. The sameness some individuals share to make up the same kind or universal.
2. n. The difference or character that marks off an individual from the rest of the same kind, selfhood.
3. n. A name or persona—the mask or appearance one presents to the world—by which one is known.
4. n. Knowledge of who one is.
5. n. algebra, computing Any function which maps all elements of its domain to themselves.
6. n. algebra An element of an algebraic structure which, when applied to another element under an operation in that structure, yields this, second element.

GNU Webster's 1913

1. n. The state or quality of being identical, or the same; sameness.
2. n. The condition of being the same with something described or asserted, or of possessing a character claimed.
3. n. (Math.) An identical equation.

WordNet 3.0

1. n. the individual characteristics by which a thing or person is recognized or known
2. n. the distinct personality of an individual regarded as a persisting entity
3. n. exact sameness
4. n. an operator that leaves unchanged the element on which it operates