I*den"ti*ty (?), n.; pl. Identities (#). [F. identité, LL. identitas, fr. L. idem the same, from the root of is he, that; cf. Skr. idam this. Cf. Item.] 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.

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.

• A name or persona by which one is known.
        This criminal has taken on several identities
  
• Knowledge of who one is.
        I've been through so many changes, I have no sense of identity.
        This nation has a strong identity.
  
• (Computing) Any function which maps all elements of its domain to themselves.
  
• (algebra) An element of an algebraic structure which, when applied to another element under an operation in that structure, yields this, second element.