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From: Webster's Revised Unabridged Dictionary (1913)

 I·den·ti·ty n.; pl. Identities
 1. The state or quality of being identical, or the same; sameness.
    Identity is a relation between our cognitions of a thing, not between things themselves.   --Sir W. Hamilton.
 2. The condition of being the same with something described or asserted, or of possessing a character claimed; as, to establish the identity of stolen goods.
 3. Math. An identical equation.