#settheory — Public Fediverse posts

RE: https://mastodon.social/@sflorg/116517535576002455

The human behavioral range, filters overlapping data segments by learned, hard encoded, and individual bias...

#BehavioralScience #Scalar #Differential #Equations #DoingTheMath #BehavioralRange #ValueTheory #SetTheory

Late to the party, but I heart “Rethinking Set Theory”, Tom Leinster’s presentation of ETCS (https://arxiv.org/abs/1212.6543). My natal foundation is higher-order logic, and this is the first time set theory has made any sense to me, other than as a technical device.

Bonus lecture notes: https://webhomes.maths.ed.ac.uk/~tl/ast/ast.pdf

#settheory #etcs #higherorderlogic

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:

https://www.infinitelymore.xyz/p/what-is-the-infinite

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

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

https://arxiv.org/abs/2411.11568

#GregoryChaitin - Is #Mathematics #Eternal?

https://www.youtube.com/watch?v=KEuylDsONxo

#Philosophy #PhilosophyOfScience #PhilosophyOfMathematics #Science #Math #Maths #Cantor #Ramanujan #SetTheory #God #Spirituality #Beauty #Transcendence #Numbers #Contradiction #Logic #Poincaré #Poincare #Euler #CloserToTruth #RobertKuhn

Interesting read about #mathematics, #settheory, and #informationtheory from Quanta Magazine, about getting closer to resolving the union-closed conjecture. It references the 1948 paper, “A Mathematical Theory of Communication" from #claudeshannon.

https://www.quantamagazine.org/long-out-of-math-an-ai-programmer-cracks-a-pure-math-problem-20230103/