/sci/ - Science & Math

>Why is the Axiom of Infinity accepted?
Axioms aren't accepted, they're assumed.

Wildberger pls go

>>10786364
Ok, then why is the axiom assumed?

The unified equation cannot be simulated without assuming infinite scope and depth. This was proven a few months ago

>>10786369
>Ok, then why is the axiom assumed?
To prove theorems..

>>10786361
>Shouldn’t axioms be intuitive free from controversy?
No.

>>10786369
Because a few months ago humanity developed a program that simulates all of physics from a single equation and the simulation does not worth if infinite depth and scope are not axioms of the computations.

>>10786401
What are you talking about

>>10786369
>>10786361
are you seriously denying infinite sets exist? Surley you think there are infinite natural numbers right? If not you have to prove wehere numbers stop and integrate that into a higher set theory.

>>10786361
>why is the axiom necessary to describe reality or solve problems?
because there are infinite numbers. ie you can always do something one more time. For example if infinite prime numbers didnt exist, there would be a largest one, which is a contradiction.
>Shouldn’t axioms be intuitive and free from controversy?
no, plenty of these set theoretical axioms are controversial
>Why is the Axiom of Infinity accepted?
Its the easiest and most intuitive way to deal with infinite sets

Because setting arbitrary limits is even dumber.

>>10786415
Why do I have to prove what is the last number? Isn’t it possible that we just don’t know what it is?
>>10786429
But you can’t actually keep adding to numbers. Even if you spent the rest of your life manipulating symbols, then you would eventually stop. If all human efforts were spent just trying to create a really large number, then eventually, we would all be dead, and there actually would be one last number. There is no contradiction arising from rejecting the existence of infinite integers

>>10786409

Optimuminstitute.org and fyi, many people have keyword triggers for that websites mention. Hunting this theories researches is like Academias version of Jewwatch, because optimum theory destroys the curve, but they will get over it eventually. Take a look. What you are seeing there is real and nothing will be the same. Cheers

>>10786441
>Isn’t it possible that we just don’t know what it is?
you have to prove its there at least, and you have to prove that adding one to it dosent get you a number
>But you can’t actually keep adding to numbers
sure you can
>If all human efforts were spent just trying to create a really large number
you dont create numbers, you describe them. You would have to prove that there is no way to describe some numbers. Which is by definition, impossible, because in doing this you would have to single out some number thereby describing it.
>manipulating symbols
mathematical formalism is retarded, math resides in collective subconscious.
>There is no contradiction arising from rejecting the existence of infinite integers
Yes there is, consider godels theories. If what you are saying is true, then there is a possibility for some godel numbering to be "correct" in that, somewhere down the line, since there is only finite numbers, for there to be complete formal system. The only way then, to find true mathmatical truths would be to just brute force through literally every single godel number applied to every theroem possible in math.

>>10786463

Website is shit... they are still trying to figure out an income model that makes sense, but complete course is free at the moment and is what it claims. At last, its unified physics. They will, and do, say we do not deserve this knowledge, but fuck the Boomers (i love the Boomers, but they need to accept that their models are old) cheers

>>10786489

Hmmm...

>>10786361
There are systems with no caps on states

>>10786489
Gary, you are such an autistic fuck. Nobody gives a shit about your lunatic political ranting and your unified equation is ridiculous on so many levels. You completely failed to produce even one coherent original thought and are a total maniac. cheers

>>10786726
>Gary, you are such an autistic fuck. Nobody gives a shit about your lunatic political ranting and your unified equation is ridiculous on so many levels. You completely failed to produce even one coherent original thought and are a total maniac. cheers

Sounds like a solid endorsement. Can this be in the opening quotes for the Optimum Theory 2020 video? Thanxs

>>10786488
>Yes there is, consider godels theories. If what you are saying is true, then there is a possibility for some godel numbering to be "correct" in that, somewhere down the line, since there is only finite numbers, for there to be complete formal system. The only way then, to find true mathmatical truths would be to just brute force through literally every single godel number applied to every theroem possible in math.
I'm on your side but you're way off the mark here.

>>10786369
You need to assume some axioms in order to prove interesting theorems. It’s unhelpful to concentrate on minimizing the total (non redundant) axioms assumed, because the point of set theory is ultimately to provide a consistent language for describing other mathematical structures, like the integers, reals, etc, the construction of which would be impossible without axiom of infinity. Like you may be able to define basic arithmetic of natural numbers without infinity using axiom schema of replacement, but your fucked if you try to define the reals.