(philosophy) The doctrine that states of the mind and states of the brain are identical.

The state or quality of being identical.

plural of identicality

The property of being identical.

(mathematics, of a function) Being equal to the zero function and not merely zero at a particular point in its domain.

(algebra) An element of an algebraic structure, generally denoted 1, which is an identity for a multiplicative operation (generally denoted × or *, or by concatenation).

(algebra) An element of an algebraic structure, generally denoted 0, which is an identity for an additive operation (generally denoted +). That is, x + 0 = 0 + x = x for any x in the structure.

(algebra) An element of a structure that produces an identity mapping when applied on the right.

(algebra) An element of a structure that produces an identity mapping when applied on the left.

(algebra) An element of an algebraic structure which when applied, in either order, to any other element via a binary operation yields the other element.