The Axiom Schema of Replacement is a principle in set theory that asserts if you have a set and a definable function, you can create a new set containing the images of the elements of the original set under that function. This axiom allows for the construction of new sets from existing ones, enhancing the power of set theory by ensuring that operations on sets can yield valid results. It plays a crucial role in formalizing mathematical constructs and connects deeply with the foundational Zermelo-Fraenkel axioms, as well as with concepts like the Axiom of Choice.
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