identity

noun

Etymology: From Middle English ydemptite, from Middle French identité and its etymon Late Latin idemptitās, identitās, from idem (“the same”) + -tās (suffix forming abstract nouns) as a calque of Ancient Greek ταὐτότης (tautótēs, “sameness”).

1. Sameness, identicalness; the quality or fact of (several specified things) being the same.

   “But whenas a leſſer number of Agreements in each Paralleliſm (provided there were nothing contrary) could not but have been a ſtrong preſumption of the Identity of the Subjects of the Viſions in each Chapter, I mean, That the Two-horned Beaſt and the Whore are one, and the Seven-headed Beaſt in each Chapter the ſame; how fully aſſured muſt we needs be of theſe Identities, the Agreements of theſe two Paralleliſms (thoſe paſſages onely excepted of which I have given ſo fair an account) perfectly exhauſting the whole ſubſtance of each Chapter?”

   “[…] suggesting the two are different stages of the same species. The identity of the two species is further suggested by allozyme analysis […]”

2. The difference or character that marks off an individual or collective from the rest of the same kind; selfhood; the sense of who something or someone or oneself is, or the recurring characteristics that enable the recognition of such an individual or group by others or themselves.

   “I've been through so many changes, I have no sense of identity.”

   “This nation has a strong identity.”

3. A name or persona—a mask or appearance one presents to the world—by which one is known.

   “This criminal has taken on several identities.”

   “In this show, the competitor's identity will remain secret until after the vote.”

4. An equation which always holds true regardless of the choice of input variables.

   “The equation (x+y)(x−y) = x²−y² is an algebraic identity. It is true regardless of the values of x and y.”

5. Any function which maps all elements of its domain to themselves.
6. An element of an algebraic structure which, when applied to another element under an operation in that structure, yields this second element.

   “Zero is the identity for the addition of real numbers.”

7. A well-known or famous person.

   “The body of a well known old identity named James Conroy […] was found in the water yesterday afternoon…”