How Does the Following Definition of the Axiom of Choise Entail that Elements Are Simultaneously Chosen from an Infinite Collection of Nonempty Sets
34045
3 Statements of axiom of choice are equivalent
66301
The cardinality of the set of countably infinite subsets of an infinite set
19414
Uncountable subset with uncountable complement, without the Axiom of Choice
49709
Suppose $X$ is infinite and $A$ is a finite subset of $X$. Then $X$ and $X \setminus A$ are equinumerous
9158
Proving that a propositional theory of any cardinality has an independent set of axioms
121847
Don't we need the axiom of choice to choose from a non-empty set?
61747
Proof of exchange principle in set theory
91237
Every infinite set contains a countable subset
130771
Sets and the principle of inclusion and exclusion
9651
Cardinality of cartesian product of an infinite set with N
31212
The existence of the empty set is an axiom of ZFC or not?
83757
Is the following equivalent to the axiom of choice?
69337
Zorn's Lemma And Axiom of Choice
153634
A statment about the equivalence between the Axiom of Choice and the surjectivity of the projections.
120064
Proving that without the axiom of choice there is a set with an accumulation point that isn'tthe limit of a convergeant sequence
109926
Axiom of Regularity and infinite sequences
62936
Proving equivalencies of two versions of the Axiom of Choice