 Axiom schema of replacement

Every definable function-class maps a set-sized domain to a set-sized range. Functionality means that the defining formula assigns exactly one output to each input in the domain.

The Axiom Schema of Replacement is a fundamental concept in set theory, particularly in Zermelo-Fraenkel set theory (ZF), which forms the basis of much of modern mathematics. This axiom schema deals with the existence of sets that can be defined by a certain property or function.