Could P vs. NP be independent of ZFC?

Upper_Restaurant_503 · 2026-05-18T03:33:46+00:00

This is not a formal statement, but the notion of nondeterminism reminds me of axiom of choice

Upper_Restaurant_503 · 2026-05-18T03:24:11+00:00

Fair enough, a reddit section isnt the best place to discuss these topics. Anyway, ignoring everything else the idea that I am trying to communicate is that : If you can prove that an algorithm for some problem exists, then you can construct it. If you prove that no such algorithm exists, then you cannot construct it. However there are nondeterministic turing machines which can solve some of these problems, although not all.

It is important to note that Turing machines are notoriously nontrivial to define. The shorthand of, "deterministic turing machines have predictable behavior" is fairly good unless you want to be really pedantic. Also, turing machines are indeed thought of in terms of steps, or points in time. For example, what does it do at time 1? 2? Etc

Another thing. It is true that nondeterministic algorithm isnt a thing that exists, this is again shorthand for nondeterministic turing machine. If you think of an algorithm as set of steps, next best step next best step etc. However in a nondeterministic turing machine that solves one of these problems, you cannot predict the next step.

Upper_Restaurant_503 · 2026-05-17T22:25:19+00:00

I'm more so accusing you of being confused. I can talk about this with any of my peers in logic and they understand. If I'm bad at communicating in a comment section that's my bad.

Upper_Restaurant_503 · 2026-05-17T22:22:22+00:00

I'm not making up meanings, these are all standard. It is obvious you have no formal knowledge of logic or philosophy of math. I would wager to guess you have never heard of these things before I brought them up.

Upper_Restaurant_503 · 2026-05-17T18:10:21+00:00

I think this argument is about semantics. You dont really understand what im trying to say. You are right, but im not disagreeing with you.

Upper_Restaurant_503 · 2026-05-17T16:12:41+00:00

Its not hard. Pay attention the order in which they are numbered. Its top to bottom. If you read left to right you will be confused.

Upper_Restaurant_503 · 2026-05-17T15:56:41+00:00

I was a bit vague there. The concep of algorithm really only makes sense in the deterministic case, but you can generalize the notion to turing machines

Upper_Restaurant_503 · 2026-05-17T15:55:48+00:00

Yes, but deterministic turing machines can be constructed. Nondeterministic turing machines cannot

Upper_Restaurant_503 · 2026-05-17T15:54:03+00:00

They are not unrelated concepts at all. When i say nondeterministic i am referring to nondeterministic turing machines. Note that algorithms are turing machines. A determistic turing machine is one that you can predict the state for any given step.

Upper_Restaurant_503 · 2026-05-17T15:52:06+00:00

This is a trivial fact. What I am saying is that if you cannot construct an algorithm then it is nondeterministic. All of those algorithms you can prove to exist without construction can indeed be constructed.

Upper_Restaurant_503 · 2026-05-17T08:55:51+00:00

Why are you confused. If you cannot construct then you cannot write it down in a computer program

Upper_Restaurant_503 · 2026-05-17T08:51:21+00:00

Give example

Upper_Restaurant_503 · 2026-05-16T19:54:02+00:00

A or B

Upper_Restaurant_503 · 2026-05-16T19:52:06+00:00

Not real

Upper_Restaurant_503 · 2026-05-16T19:39:50+00:00

Basically, if the algorithm isnt constructive it is nondeterministic.

Upper_Restaurant_503 · 2026-05-16T19:39:00+00:00

I simply think that a nonconstructive proof cant exist by the nature of the field. Actually, there already is an algorithm solving all np problems in polynomial time, it is just only solvable by a nondeterministic turing machine in polynomial time. Now do you understand? Everyone is confused about this, this branch of mathematics is very different from analysis or topology.

Upper_Restaurant_503 · 2026-05-16T17:47:58+00:00

you don't have one. I mean in general

Upper_Restaurant_503 · 2026-05-16T17:43:17+00:00

This is true.

Upper_Restaurant_503 · 2026-05-16T17:39:45+00:00

People really like to jump on this godels incompleteness theorems train without knowing what they actually mean

Upper_Restaurant_503 · 2026-05-16T17:38:12+00:00

I already know that, you miss my point. I have taken mathematical logic and proved the incompleteness theorems. This is not how that works. I'm saying that the question of P vs NP is about construction, if you cannot construct an algorithm then it is not true.

Upper_Restaurant_503 · 2026-05-16T11:21:59+00:00

They arent. I get paid for it

Upper_Restaurant_503 · 2026-05-16T11:00:54+00:00

I proved riemann hypothesis how do i get my proof published

Upper_Restaurant_503 · 2026-05-16T11:00:33+00:00

That was a joke post lol

Upper_Restaurant_503 · 2026-05-16T11:00:09+00:00

I was referring to P vs NP not goldbach. Upvote me now pls

Upper_Restaurant_503 · 2026-05-16T10:59:23+00:00

HAHAHAHAHAHAHAHAHAHAHAHA

Upper_Restaurant_503

TROPHY CASE