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.
