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> you just build some sets to represent numbers and make operations that act the same way as arithmetic which is already "just" some non trivial problem(there
by andriy_koval 1mo ago
> you just build some sets to represent numbers and make operations that act the same way as arithmetic
which is already "just" some non trivial problem(there is no "operations" in set theory), and we are discussing if it is achievable.
- IsTom 1mo agoYou make relations and functions out of sets and prove theorems about them, reducing definition of things in terms of belonging to a set. This isn't particularly complicated.
- andriy_koval 1mo agoNo, once you start formalize this, it becomes complicated. There is a reason why looks like there is no "peano can be derived from zfc" theorem which would close dispute, and my opponents need to throw links on bro math from stackexchange in this discussion.
- IsTom 1mo agoPer https://en.wikipedia.org/wiki/Peano_axioms#Set-theoretic_models https://en.wikipedia.org/wiki/Peano_axioms#Set-theoretic_mod... > The Peano axioms can be derived from set theoretic constructions of the natural numbers and axioms of set theory such as ZF.[15] If you're going against the general consensus you should present something more than nebulous assertions that it's wrong.
- andriy_koval 1mo agoObviously citation from wikipedia can't be considered as replacement of math proof. > If you're going against the general consensus you should present something more than nebulous assertions that it's wrong. burden of proof is on the one who claims something exists.