Identity

In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B, which might contain some variables, produce the same value for all values of the variables within a certain domain of discourse. The cited article adds that an identity is an equality between functions that are differently defined, that identities are sometimes indicated by the triple bar symbol instead of the equals sign, and that formally an identity is a universally quantified equality. Theorems stated as identities, such as those relating two expressions for the same quantity, are grouped under this concept together with the wider concept of an equation.