Definition of "Identity" :

noun: the distinct personality of an individual regarded as a persisting entity

"You can lose your identity when you join the army."

noun: exact sameness

"They shared an identity of interests."

noun: 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."

noun: an operator that leaves unchanged the element on which it operates

"The identity under numerical multiplication is 1."