identity

noun7

1. •
   the things that make a person or a group who they are and set them apart from others

   • I've been through so many changes, I have no sense of identity.
   • This nation has a strong identity.
2. •
   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.
3. •
   Sameness, identicalness; the quality or fact of (several specified things) being the same.

   • Benjamin Franklin established the identity of electricity and lightning.
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. •
   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.
6. •
   Any function which maps all elements of its domain to themselves.
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