identity

Etymology

Middle French identité, from Latin idem (“the same”). See identical and idem.

noun

1. Sameness, identicalness; the quality or fact of (several specified things) being the same.
   […] suggesting the two are different stages of the same species. The identity of the two species is further suggested by allozyme analysis […] 1997, “Hydrothermal Vent Fauna”, in Advances in Marine Biology: The Biogeography of the Oceans, page 111
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 themself.
   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. (mathematics) 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. (algebra, computing) Any function which maps all elements of its domain to themselves.
6. (algebra) An element of an algebraic structure which, when applied to another element under an operation in that structure, yields this second element.
7. (Australia, New Zealand) A well-known or famous person.
   The body of a well known old identity named James Conroy […] was found in the water yesterday afternoon… 1887 July 19, “Drowned at Williamstown”, in The Age, Melbourne
   April 4 2013, “Cricket identities consult lawyers”, in New Zealand Herald:
   January 13 2016, “Kings Cross identities arrested in connection with murder”, in The Sydney Morning Herald: