What is Zermelo-Fraenkel set theory?

Q: What is Zermelo-Fraenkel set theory?


A: Zermelo-Fraenkel set theory, also known as ZF, is a system of axioms that is used to describe set theory.

Q: What is the system of axioms used in set theory by most mathematicians today?


A: The system of axioms used in set theory by most mathematicians today is ZFC, which is Zermelo-Fraenkel set theory with the axiom of choice added.

Q: Why was Zermelo-Fraenkel set theory proposed?


A: Zermelo-Fraenkel set theory was proposed to describe set theory without contradictions, after Russell's paradox was discovered in 1901.

Q: Who proposed the theory of set theory in 1908?


A: Ernst Zermelo proposed the theory of set theory in 1908.

Q: Who proposed a new version of Zermelo's work in 1922?


A: Abraham Fraenkel proposed a new version of Zermelo's work in 1922.

Q: What was the motivation for mathematicians to find a way to describe set theory without contradictions?


A: The motivation for mathematicians to find a way to describe set theory without contradictions was the discovery of Russell's paradox in 1901.

Q: What is ZFC?


A: ZFC is the system of axioms used in set theory by most mathematicians today, which is Zermelo-Fraenkel set theory with the axiom of choice added.

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