Theoretical Identity

A theoretical identity is a fundamental, always-true statement within a particular mathematical or logical system that expresses an equivalence between two expressions. It holds universally within that context, meaning no matter what specific values or situations are involved, the identity remains valid. For example, in algebra, "a + 0 = a" is a theoretical identity because it is always true for any number 'a'. These identities help simplify complex problems and establish consistent rules, forming the foundation for more advanced theory and reasoning within various fields.