For ten points identify thios postulate of set theory which dictates that, in any collection of nonempty sets C, there exists a function f such that one can choose any set S and find f of S to be a member of S.
One of Hilbert's Problems concerns this assertion, which has yet to be proven or disproven; the first serious attempt was by Russell in the Principia Mathematica. Gödel demonstrated in his 1937 proof of Incompleteness Theorem that it could verifiably not be derived from the 9 more conventional Zemerlo­Fraenkel Axioms, nor could any of them be derived from it alone. It is often called Tychonoff's Theorem or Zorn's Lemma, especially in the context of its generation of non­integrable functions. For ten points identify thios postulate of set theory which dictates that, in any collection of nonempty sets C, there exists a function f such that one can choose any set S and find f of S to be a member of S.
One of Hilbert's Problems concerns this assertion, which has yet to be proven or disproven; the first serious attempt was by Russell in the Principia Mathematica.
Axiom of Choice (accept Zorn’s Lemma and prompt on Tychonoff’s Theorem (which has to be generalized to be synonymous with AC) before they are mentioned.