identity

Noun

Synonyms: personal identity individuality identity element identity operator identicalness indistinguishability

WordNet 3.0

Noun (4)

the distinct personality of an individual regarded as a persisting entity“you can lose your identity when you join the army”Synonyms: personal identity individuality
the individual characteristics by which a thing or person is recognized or known“geneticists only recently discovered the identity of the gene that causes it”“it was too dark to determine his identity”“she guessed the identity of his lover”
an operator that leaves unchanged the element on which it operates“the identity under numerical multiplication is 1”Synonyms: identity element identity operator
exact sameness“they shared an identity of interests”Synonyms: identicalness indistinguishability

Webster's Dictionary (GCIDE)

Identity \I*den"ti*ty\, n.; pl. Identities. [F. identit['e], 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. [1913 Webster]

Identity is a relation between our cognitions of a thing, not between things themselves.— Sir W. Hamilton.[1913 Webster]

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. [1913 Webster]

3.(Math.) An identical equation. [1913 Webster]