identity

1. (mathematics) An equation which always holds true regardless of the choice of input variables.Examples: "The equation (x+y)(x−y) = x²−y² is an algebraic identity. It is true regardless of the values of x and y."Synonyms: identity functioncountableuncountable

2. (algebra, computing) Any function which maps all elements of its domain to themselves.countableuncountable

3. (algebra) An element of an algebraic structure which, when applied to another element under an operation in that structure, yields this second element.Examples: "Zero is the identity for the addition of real numbers."countableuncountable

4. (Australia, New Zealand) A well-known or famous person.Examples: "The body of a well known old identity named James Conroy […] was found in the water yesterday afternoon…"Synonyms: celebrity, personalityAustraliaNew-Zealandcountableuncountable