In mathematics an identity is an equality relation A = B, such that A and B contain some variables and A and B produce the same value as each other regardless of what values (usually numbers) are substituted for the variables. In other words, A = B is an identity if A and B define the same functions. This means that an identity is an equality between functions that are differently defined. For example (a + b)²  =  a² + 2ab + b² and are identities. Identities are sometimes indicated by the triple bar symbol = instead of =, the equals sign.