Axiom of Choice

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Definition

Given a (possibly) infinite collection of nonempty sets, we can form a new set that contains one (random) element from each set.

We do not know, which element was chosen.

Discussion

The Axiom of Choice is controversial and gives rise to paradoxes like the non-measurable set or the Banach-Tarski Paradoxon

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Appendix

• Tags:
  • Zermelo-Fraenkel Set Theory
  • Set Theory
• Reference:
  • + 2022-04-19 How the Axiom of Choice Gives Sizeless Sets

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