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#zfc — Public Fediverse posts

Live and recent posts from across the Fediverse tagged #zfc, aggregated by home.social.

  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. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. Not been getting out to photograph much this last year. Need to change that so was glad just to get out and make these photos yesterday in Bridgwater in Somerset. #nikon #photography #zfc #Somerset #bridgwater

  8. It seems one can represent ZFC (or any other logic or type system) as Lean 3's GADT. Note that binder very elegantly represented as HOAS. Am I first who discovered this? #types.pl #plt #lean #lean3 #gadt #zfc #hoas

    lobste.rs/s/11k4ri/how_should_

  9. It seems one can represent ZFC (or any other logic or type system) as Lean 3's GADT. Note that binder very elegantly represented as HOAS. Am I first who discovered this? #types.pl #plt #lean #lean3 #gadt #zfc #hoas

    lobste.rs/s/11k4ri/how_should_

  10. It seems one can represent ZFC (or any other logic or type system) as Lean 3's GADT. Note that binder very elegantly represented as HOAS. Am I first who discovered this? #types.pl #plt #lean #lean3 #gadt #zfc #hoas

    lobste.rs/s/11k4ri/how_should_

  11. It seems one can represent ZFC (or any other logic or type system) as Lean 3's GADT. Note that binder very elegantly represented as HOAS. Am I first who discovered this? #types.pl #plt #lean #lean3 #gadt #zfc #hoas

    lobste.rs/s/11k4ri/how_should_

  12. It seems one can represent ZFC (or any other logic or type system) as Lean 3's GADT. Note that binder very elegantly represented as HOAS. Am I first who discovered this? #types.pl #plt #lean #lean3 #gadt #zfc #hoas

    lobste.rs/s/11k4ri/how_should_

  13. Dear #lazyweb, I’m falling in love for the #Nikon #zfc but I can’t decide. I do have a Nikon camera (D7000 if you have seen my pictures) and it’s not going away, and I have both a 18-50 and 50-200. So my questions in the poll :) I appreciate any help, and please comment for your rationale and experience! I like the black edition but I can’t help thinking the silver is more peculiar, but I don’t like the kit 16-50 in silver… so I’m a bit oriented to get silver + 28 + adapter #photocamera