Zermelo–Fraenkel Set Theory...
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MATHEMATICS
Set Theory
Zermelo–Fraenkel Set Theory with Choice (ZFC)
A single axiom transformed the foundations of mathematics and resolved paradoxes
7 days ago
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Why is the axiom of choice considered essential in Zermelo–Fraenkel set theory with choice (ZFC)?
Because it eliminates all paradoxes in set theory by restricting set formation.
Because it enables the proof of fundamental theorems like every vector space having a basis and the well-ordering theorem.
Because it explicitly constructs all sets required in mathematical proofs.
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