Cardinal numbers
Cardinal number
- https://en.wikipedia.org/wiki/Cardinal_number
- Cardinal numbers are a group of object, where their order (greater or equal to) and arithmetic are all defined by operations of the seat each of them represent
Ordinal numbers
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
- 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
