Equality (mathematics)
Identities

An identity is an equality that is true for all values of its variables in a given domain. An "equation" may sometimes mean an identity, but more often than not, it specifies a subset of the variable space to be the subset where the equation is true. An example is (x + 1) (x + 1) = x 2 + 2 x + 1 {\displaystyle \left(x+1\right)\left(x+1\right)=x^{2}+2x+1} is true for all real numbers x {\displaystyle x}. There is no standard notation that distinguishes an equation from an identity, or other use of the equality relation: one has to guess an appropriate interpretation from the semantics of expressions and the context. Sometimes, but not always, an identity is written with a triple bar: (x + 1) (x + 1) ≡ x 2 + 2 x + 1. {\displaystyle \left(x+1\right)\left(x+1\right)\equiv x^{2}+2x+1.}
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