Mathematics/About an elementary question of the theory of diversity [Set Theory]

Cardinal numbers

Cardinal number

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Ordinal numbers

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Axiom of choice

Definition

  • Informally put, the axiom of choice says that given any collection of sets, each containing at least one element, it is possible to construct a new set by choosing one element from each set, even if the collection is infinite
  • Included in the Zermelo-Fraenkel axioms
  • With this axiomo we can prove the Banach Tarski paradox
  • https://www.youtube.com/shorts/e28mB2DU_ZI

Cantor's theorem

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  • Consequently, the theorem implies that there is no largest cardinal number (colloquially, "there's no largest infinity")

Cantor's diagonal argument

Proof that the real numbers are uncountable

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Written by Davi Cavalcanti Sena who lives and works in Vancouver building useless things