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 range of validity.[1] In other words, A = B is an identity if A and B define the same functions, and an identity is an equality between functions that are differently defined. For example, and are identities.[1] Identities are sometimes indicated by the triple bar symbol ≡ instead of =, the equals sign.[2] Formally, an identity is a universally quantified equality.