1.  identity(n = noun.attribute) individuality, personal identity - the distinct personality of an individual regarded as a persisting entity; "you can lose your identity when you join the army"
is a kind of personality
has particulars: gender identity, identification, personhood
Derived form verb identify₁

2.  identity(n = noun.cognition) - 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"
is a kind of identification, recognition
Derived forms verb identify₁, verb identify₅, verb identify₂

3.  identity(n = noun.linkdef) identity element, identity operator - an operator that leaves unchanged the element on which it operates; "the identity under numerical multiplication is 1"
is a kind of operator

4.  identity(n = noun.attribute) identicalness, indistinguishability - exact sameness; "they shared an identity of interests"
is a kind of sameness
has particulars: oneness, unity, selfsameness
Derived forms adjective identical₁, adjective identical₂, verb identify₆, verb identify₃

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." [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.  An identical equation. [1913 Webster]

identity, n. (pl. -ies)
1 a the quality or condition of being a specified person or thing. b individuality, personality (felt he had lost his identity).
2 identification or the result of it (a case of mistaken identity; identity card).
3 the state of being the same in substance, nature, qualities, etc.; absolute sameness (no identity of interests between them).
4 Algebra a the equality of two expressions for all values of the quantities expressed by letters. b an equation expressing this, e.g. (x + 1)(2) = x(2) + 2x + 1.
5 Math. a (in full identity element) an element in a set, left unchanged by any operation to it. b a transformation that leaves an object unchanged.

Idiom:
identity crisis a phase in which an individual feels a need to establish an identity in relation to society. identity parade = identification parade.

Etymology:
LL identitas f. L idem same

N  identity, sameness, coincidence, coalescence, convertibility, equality, selfness, self, oneself, identification, monotony, tautology, facsimile, homoousia: alter ego, ipsissima verba, same, self, very, one and the same, very thing, actual thing, real McCoy, no other, one and only, in the flesh, identical, self, ilk, the same, selfsame, one and the same, homoousian, coincide, coalescent, coalescing, indistinguishable, one, equivalent, tweedle dee and tweedle dum, much the same, of a muchness, unaltered, identically, on all fours.

N  equality, parity, coextension, symmetry, balance, poise, evenness, monotony, level, equivalence, equipollence, equipoise, equilibrium, equiponderance, par, quits, a wash, not a pin to choose, distinction without a difference, six of one and half a dozen of the other, tweedle dee and tweedle dum, identity, similarity, equalization, equation, equilibration, co-ordination, adjustment, readjustment, drawn game, drawn battle, neck and neck race, tie, draw, standoff, dead heat, match, peer, compeer, equal, mate, fellow, brother, equivalent, equal, even, level, monotonous, coequal, symmetrical, coordinate, on a par with, on a level with, on a footing with, up to the mark, equiparant, equivalent, tantamount, indistinguishable, quits, homologous, synonymous, resolvable into, convertible, much at one, as broad as long, neither more nor less, much the same as, the same thing as, as good as, all one, all the same, equipollent, equiponderant, equiponderous, equibalanced, equalized, drawn, half and half, isochronal, isochronous isoperimetric, isoperimetrical, isobath, isobathic, equally, pari passu, ad eundum, caeteris paribus, in equilibrio, to all intents and purposes, it comes to the same thing, it amounts to the same thing, what is sauce for the goose is sauce for the gande.

gender identity, identity card, identity crisis, identity element, identity matrix, identity operator, identity theft, identity verification, personal identity