The Zermelo-Fraenkel Axioms (ZF) are a set of axioms for set theory that provide a formal foundation for mathematics. These axioms aim to avoid paradoxes like those found in naive set theory by clearly defining how sets can be constructed and manipulated. ZF is crucial in establishing the consistency and independence of mathematical theories, as well as addressing issues such as Cantor's Paradox, which highlights limitations in naive approaches to sets.
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