Identity

The state or quality of being identical, or the same; sameness.

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.

An identical equation.

an operator that leaves unchanged the element on which it operates; "the identity under numerical multiplication is 1"

the distinct personality of an individual regarded as a persisting entity; "you can lose your identity when you join the army"

exact sameness; "they shared an identity of interests"