>be me>just a guy>notice that tools for modeling reality should probably be based on reality>reality is finite>so why does all of mathematics assume infinity exists>not prove it>assume it>and not even a recent assumption>predates written history>some prehistoric human looked at the horizon and thought "that goes on forever">we built calculus on it>decide infinity doesn't exist >and >that there is an upper bound>axiom>moving on>rebuild all of math>normal weekend>invent new logic where every quantifier must declare its finite range>turns out cleaner>mathematicians were just lazy>seven axioms of new set theory>exclude Power Set, Axiom of Infinity, unrestricted Choice>each one gets a formal obituary>rebuild entire number chain with explicit finite bounds>natural, integer, rational, real, complex>all of it works>just honest now instead of hiding bounds in infinity>classical math called that hiding "elegance">it was a prehistoric assumption in a tuxedo>recover all of analysis, sort all classical theorems into four buckets>most survive, three specific theorems live in a precisely characterised gap>physics chapter: infinity is scaffolding, universe has holographic bound, universe agrees with me>universe hasn't emailed>all 7 Millennium Problems addressed>none solved, I'm just a guy>200 pages done>can't publish, not an academic>shakyfoundation.com>$30/year>turns out infinity isn't the only prehistoric assumption I think is wrong>there are others>addressing them one at a time>in my spare time>on a $30 domain>nobody asked>you're welcome
>be menigga who elsedidnt read the rest of that shit
Godelsget fucked
Gödel's incompleteness theorems apply to systems that can express arithmetic and are consistentBST can express arithmeticso yes, BST is incompletejust like ZFC is incompletejust like every sufficiently powerful formal system is incompleteGödel didn't kill ZFCGödel didn't kill Peano ArithmeticGödel didn't kill BSTalsoincompleteness means there exist true statements unprovable within the systemBST already has a precisely characterised gap — Category DGoodstein, Paris-Harrington, Ackermann totalitythe gap is already named and documented"Gödel" is not a magic word that makes foundations disappearit's a result that applies to literally every foundation including the one you're currently using
What are these "new foundations" for? Can it prove 0.999... != 1 or Collatz?
>>16929819>notice that tools for modeling reality should probably be based on realityThat's not a "notice" situation, that's an assertion.>reality is finiteProve it.>there is an upper boundLet n be your upper bound.How does your system handle n+1?
>>16929819NIGGERS like you will use some LLM and believe themselves to have found the answers to the universe and everything, but i can't FULLY fault (you), for most LLM's are constructed purposefully wrong in a very pernicious way, for it does seem that they have been built to suckle on the anus of whichever "person" that doth cast their nonsense onto them, at last, finitary set theory is a VERY well trodden topic, (you)'d do well, where you to be an actual human, to actually inform yourself on the matter, rather than let some LLM to do the speaking and/or thinking for (you), for if any of us would wish to hear what some LLM has to "say", we'd just "ask" it ourselves, (you) are an intrinsically superfluous middlemen, and your services will NEVER be required by anyone, take care, and have a lovely day ;)
>>16929819Very interesting work. I haven't looked at it in detail but I have similar ideas.
0.999...=1 holds in BST — Cauchy completion doesn't need infinity. On n+1: the bound is metatheoretic, outside the system, same move ZFC makes with proper classes. On "prove reality is finite": nobody proved infinity exists either. Collatz is open in every foundation including this one.
Finitary set theory is well trodden — and every prior attempt hit the same wall. No rigorous foundation. Kronecker, Nelson, the ultrafinitists — right intuition, couldn't build on it. The contribution isn't the idea, it's that the foundation now exists.
>>16929863i cast probability theory onto you.>the chances of your theory being this gigantic thing you think of it is.. 1%sorry bud. those are the rules of the game which you wish to demolish so anxiously
I'm very well aware that the chanses are miniscule. You're being very very generous with the 1%I'm just hoping that someone who actually knows their stuff would take a serious look.There's a Coq proof on github if that helps.
>>16929845you change the language so that you can describe results that were unspeakable in your old formalism
Yes, the "language" had to change as First Order Logic allows for infinite Cardinals and Ordinals. can't have that in a finite framwork or infinity just comes back in, which is what seperates my idea from ZF°.ZF° still relies on First Order Logic, which allows for infinity
>>16929868>I'm just hoping that someone who actually knows their stuff would take a serious look.You should post it somewhere else then
>>16929926Oh, I am ;)One doesn't exclude the other though, regardless of how much you hate it.
Thank YouForYourTime
>>16929939You're welcome!Although, 4chan... All your obejctions so far has been thourouly explained in the paper. You're the lazy ones so far, not me
>>16929819you didn't rebluild all of math anon.
>>16929819LLM niggers btfo.
I always find it funny that constructivists are the ones who obsess over metaphysics while all other flavours of mathematicians be it platonists or formalists or whatever else just ignore it and focus on doing maths.Constructivists try to frame themselves as the grounded ones that are the solution to Platonic madness and yet they're the ones who have this religious obsession over stuff that ultimately does not matter when actually doing maths. Infinity is useful in real life, that's why most people use it regardless of their belief on whether infinity is ontic or not.>can't publish, not an academicThat is blatantly untrue. If your idea is solid, there are dozens of academics salivating at the idea of stealing it and including you as a coauthor. The nuance here is that most of the time it's just incomprehensible schizo ramblings.
>>16929991>The nuance here is that most of the time it's just incomprehensible schizo ramblings.in the defence of OP , maybe his ideas have merits because he really can't share them because they are schitzo rambelings.
I do not care for models that not allow infinite sets to be modeled by finite ones.
