Axiom of Choice
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MATHEMATICS
Set Theory
Axiom of Choice
Infinite selections made possible by a single bold assumption
21 hours ago
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Why was the axiom of choice introduced in set theory?
To guarantee the ability to select one element from each set in any collection, even infinite ones
To prove that all sets are finite
To show that no infinite sets exist
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MATHEMATICS
Set Theory
Axiom of Choice
A single axiom unlocks infinite selections without explicit rules
8 days ago
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Why does the axiom of choice challenge traditional notions of constructibility in mathematics?
Because it asserts the existence of selection sets without providing a method to explicitly construct them.
Because it only applies to finite collections of sets, which are easy to construct.
Because it denies the existence of infinite sets altogether.
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