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In mathematics, this usually refers to some form of the principle, going back to Leibniz, that two mathematical objects are equal if there is no test to distinguish them.

In axiomatic set theory, extensionality is expressed in the axiom of extension, which states that two sets are equal if and only if they contain the same elements. In lambda calculus, extensionality is expressed by the eta-conversion rule, which allows conversion between any two expressions that denote the same function.