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#zfc — Public Fediverse posts

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  1. So we have { 1, 2 } ∈ Fin₁ ⊆ Fin₁ₐ ⊆ Fin₂ ⊆ Fin₃ ⊆ Fin₄ ⊆ Fin₅ ⊆ Fin₆ ⊆ Fin₇

    If a set is in Fin₁ then it is considered finite by all the other definitions.

    But since the axiom of choice is equivalent to saying every set can be well-ordered, if we accept it VII-finite sets are equinumerous with a finite ordinal and so Fin₇ ⊆ Fin₁ and so the differences between these definitions collapse and ZF becomes ZFC, which is a widely accepted basis for Set Theory.

    My consultation with math resources was inspired by a blog post:

    infinitelymore.xyz/p/what-is-t

    #Metamath #ZFC #SetTheory #AxiomOfChoice #FiniteSet #Infinity

  2. Any #mathematics professors want to take a shot at explaining to someone with say a typical math major undergrad background what the deal is with the recent introduction of exacting and ultraexacting cardinals?

    #math #maths #settheory #zfc

    arxiv.org/abs/2411.11568