noun Sameness, identicalness; the quality or fact of (several specified things) being the same.
Benjamin Franklin established the identity of electricity and lightning.
noun 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.
noun 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.
noun An equation which always holds true regardless of the choice of input variables.
The equation (x+y)(x−y) = x−y is an algebraic identity. It is true regardless of the values of x and y.
noun Any function which maps all elements of its domain to themselves.
noun 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.