Identity

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.
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.