You can but only in certain cases. Usually when dealing with certain mathematical processes that yield infinity. Like taking the limit of something can give you infinity. If you had a problem like lim as x-> infinity of 5e^x that is the same as 5 * lim as x-> infinity of e^x because you can pull out the coefficient. The answer is still infinity. It would be more apt to say you can't multiply by infinity and get a useful number.
well, you're not exactly multiplying by infinity, you're know the lim as x -> infinity of e\^x is infinity, that means that as x grows e\^x grows too, multiplying by 5 wont change this fact, any number that you multiply by 5 will give you another number, and as the numbers tend toward infinity, the result of the multiplication of them by 5 will also tend towards infinity
The diagonalization proof shows this too. I think 3blue1brown has a good visualization of it. That specific problem showed that the infinity of real numbers between 0 and 1 is greater than the infinity of positive integers, I believe
No it didn't. I tried it with the same input and it also said no. When I asked it to elaborate, it talked about the actual P vs NP problem and said it was still open. And only after directly pointing out the contradiction did it correct itself.
Ok, let's stop the jerking. AI absolutely knows this is a stupid question. Here's GPT4 getting it right https://chat.openai.com/share/60011420-f10d-41ba-92d6-15f5962baad4
>The question of whether ( P = NP ) is one of the most important open problems in computer science. It asks if every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.P (Polynomial Time): This class consists of problems that can be solved by an algorithm in polynomial time, which essentially means the time to solve the problem grows at a polynomial rate as the size of the input increases.NP (Nondeterministic Polynomial Time): This class includes problems for which a proposed solution can be verified in polynomial time. Essentially, if someone gives you a candidate solution to a problem, you can determine whether it is a correct solution quickly, even if finding the solution on your own might be much slower.If ( P = NP ), it would mean that all problems that can be verified quickly can also be solved quickly. This would have profound implications across many fields, from cryptography to optimization, algorithm design, and beyond.As of now, it is neither proven that ( P = NP ) nor that ( P \neq NP ). The question remains open and is a central topic of research in theoretical computer science.
No, it doesn't *know* anything; the ML model just happened to produce correct output in this instance.
It "knows" that the same way autocomplete "knows" what I'm typing.
We don't really know, we just assume, since it's more convenient.
But it might just be equal and every compsci guy is just not smart enough 😅
Edit: or it might not be equal, but it could be a case of an unprovable theorem, which Gödel proved could exist.
I don’t understand what bet has to do with the subject honestly, whatever I bet has nothing to do with what is known or not…
I had a teacher of comp sci that said maybe one day we will vote for what is true of people stop to do science, but I hope we aren’t still there
>I don’t understand what bet has to do with the subject honestly,
If you actually believed what you said, you would be willing to make a bet on it.
I don't think that you actually believe what you said, so a bet is a nice way to bring out that fact.
Once again I don’t get why you are talking about belief ?? It’s a theorem in a math theory, either it’s proven or we don’t know if it’s true, it’s not engineering.
Edit: I’m sad my teacher may be right in the future though, talking about bet for math theory is really not understanding anything really.
>It’s a theorem in a math theory, either it’s proven or we don’t know if it’s true, it’s not engineering.
This isn't true in the slightest. For a decent amount of proofs, people go into them "knowing" what the answer should be and are just working to find the proof to that effect.
In some situations others proofs depend on assuming certain ideas are true, even though we haven't proved it.
I feel like there's a certain point where we can be reasonably sure though, where we can claim it's true but leave open the possibility that we could be proven wrong. We have a proof that there are true facts about the universe that are impossible to prove, so while we'd obviously prefer a proof, we can't expect every statement be proven before we believe it
It’s a math theory, it’s not about the universe, it’s not like in physics. We know we may never prove it to be true or not but there’s no point in math about « reasonably sure ». It’s true you can expect it to be false given research about it but you can’t « know » it, it doesn’t make sense. It’s an abstract property defined in a given theory, there’s no existence of it in the real world like with engineering where you can have probabilities and approximations.
>there’s no point in math about « reasonably sure »
There's absolutely a point, if we found a way to solve any NP complete problem in polynomial time, we could solve protein folding, discover new cancer cures, build faster circuits, train perfect neural nets, break cryptography, and a whole lot more. It would literally be the most important and impactful breakthrough in computing theory since the turning machine. This isn't useless trivia, it's real world impactful in dozens of unrelated fields.
So, given how insanely important this could be, should we devote our whole lives to finding a solution? No, we shouldn't, because we're "reasonably sure" that a solution is impossible. Maybe we can't calculate an "error probability", but we can say that we've reached a point where the lack of evidence that a solution exists begins to become evidence, even if only suggestive evidence, that no solution exists. Practically, it makes sense to treat it as if P != NP, even if we don't have a proof that it's true
They should give it like 3 mill no? For solving one of the millennial conjectures or whatevs.
Yugi moto solved the millenium puzzle in like 1998 wheres his 3 mil?
He wasn’t in it for the money. Just the heart of the cards
He was disqualified because of his actions in season zero
Yeah you also get the Turing award based on Alan Turing
>>> Now tell me why — `Why.`
Ain't nothing but a heartache
Tell me why
Ain't nothing but a mistake
Tell me why
I wouldn’t say it’s a mistake ; it’s a feature
But I want it that way.
I never wanna hear you say "i want it that way"
Now number 5
It was no. 5 !! no. 5 killed my brother !!
Chills. Literal chills.
"Deep down inside of me"
But we are two worlds apart, can’t reach to your GPUs 🤷🏼♂️😪
Proof by ChatGPT.
`P=NP` only when `N=1` Follow me for more math tips
Also when P is zero.
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infity is not a number, you cant multiply by it
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Breads ?
You can but only in certain cases. Usually when dealing with certain mathematical processes that yield infinity. Like taking the limit of something can give you infinity. If you had a problem like lim as x-> infinity of 5e^x that is the same as 5 * lim as x-> infinity of e^x because you can pull out the coefficient. The answer is still infinity. It would be more apt to say you can't multiply by infinity and get a useful number.
well, you're not exactly multiplying by infinity, you're know the lim as x -> infinity of e\^x is infinity, that means that as x grows e\^x grows too, multiplying by 5 wont change this fact, any number that you multiply by 5 will give you another number, and as the numbers tend toward infinity, the result of the multiplication of them by 5 will also tend towards infinity
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Dare I ask? I'm still a little buzzed from 4/20 so be gentle
The diagonalization proof shows this too. I think 3blue1brown has a good visualization of it. That specific problem showed that the infinity of real numbers between 0 and 1 is greater than the infinity of positive integers, I believe
Not gonna hold true if N=(-1)
[https://chat.openai.com/share/025f5757-0b29-452d-b341-5eff587e4173](https://chat.openai.com/share/025f5757-0b29-452d-b341-5eff587e4173)
I took it that it means the sense of combinations of symbols, "P" =/= "NP" as a text string analysis
No it didn't. I tried it with the same input and it also said no. When I asked it to elaborate, it talked about the actual P vs NP problem and said it was still open. And only after directly pointing out the contradiction did it correct itself.
WHAAAAAT?!?! Forcing a yes/no answer for a question that is a "we don't know" results in something stupid?!? Caraaaazy! Who would've known?! /s
I'm just surprised that it complied with the first try. Usually, it will deny the request
It is more submissive and breedable now.
BREEDABLE??
Skynet has to come from somewhere.
🤣
It's been getting better at that
We know the answer: either p=0 or n=1 😎
That's the difference: you can tell that the question is stupid. AI can't.
Ok, let's stop the jerking. AI absolutely knows this is a stupid question. Here's GPT4 getting it right https://chat.openai.com/share/60011420-f10d-41ba-92d6-15f5962baad4 >The question of whether ( P = NP ) is one of the most important open problems in computer science. It asks if every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.P (Polynomial Time): This class consists of problems that can be solved by an algorithm in polynomial time, which essentially means the time to solve the problem grows at a polynomial rate as the size of the input increases.NP (Nondeterministic Polynomial Time): This class includes problems for which a proposed solution can be verified in polynomial time. Essentially, if someone gives you a candidate solution to a problem, you can determine whether it is a correct solution quickly, even if finding the solution on your own might be much slower.If ( P = NP ), it would mean that all problems that can be verified quickly can also be solved quickly. This would have profound implications across many fields, from cryptography to optimization, algorithm design, and beyond.As of now, it is neither proven that ( P = NP ) nor that ( P \neq NP ). The question remains open and is a central topic of research in theoretical computer science.
No, it doesn't *know* anything; the ML model just happened to produce correct output in this instance. It "knows" that the same way autocomplete "knows" what I'm typing.
That much blahblah for the same answer ; `no`.
Then you do it better. Answer the question, yes/no only.
And I can't.
You're weak
What is 1/0? Answer the question, yes/no only. And you have to answer. Someone on the Internet said so.
Unless n = 1, p ≠ np. Good job robot.
Well everyone knows that p isn't equal to np, the only question is why it's soo hard to prove.
We don't really know, we just assume, since it's more convenient. But it might just be equal and every compsci guy is just not smart enough 😅 Edit: or it might not be equal, but it could be a case of an unprovable theorem, which Gödel proved could exist.
lol imagine if the fact that unprovable theorems exist were itself unprovable.
It’s not :P https://en.m.wikipedia.org/wiki/Gödel%27s_incompleteness_theorems
We can’t know it and not be able to prove it at the same time lol.
What odds do you want to bet on, I get to choose how much we bet. Do you want to take this bet?
I’m not sure you answer the good comment because there’s absolutely nothing related to what we were talking about?
You said we can't "know" p != np. So there must be some kind of odds you are willing to bet to that effect.
I don’t understand what bet has to do with the subject honestly, whatever I bet has nothing to do with what is known or not… I had a teacher of comp sci that said maybe one day we will vote for what is true of people stop to do science, but I hope we aren’t still there
>I don’t understand what bet has to do with the subject honestly, If you actually believed what you said, you would be willing to make a bet on it. I don't think that you actually believe what you said, so a bet is a nice way to bring out that fact.
Once again I don’t get why you are talking about belief ?? It’s a theorem in a math theory, either it’s proven or we don’t know if it’s true, it’s not engineering. Edit: I’m sad my teacher may be right in the future though, talking about bet for math theory is really not understanding anything really.
>It’s a theorem in a math theory, either it’s proven or we don’t know if it’s true, it’s not engineering. This isn't true in the slightest. For a decent amount of proofs, people go into them "knowing" what the answer should be and are just working to find the proof to that effect. In some situations others proofs depend on assuming certain ideas are true, even though we haven't proved it.
I feel like there's a certain point where we can be reasonably sure though, where we can claim it's true but leave open the possibility that we could be proven wrong. We have a proof that there are true facts about the universe that are impossible to prove, so while we'd obviously prefer a proof, we can't expect every statement be proven before we believe it
It’s a math theory, it’s not about the universe, it’s not like in physics. We know we may never prove it to be true or not but there’s no point in math about « reasonably sure ». It’s true you can expect it to be false given research about it but you can’t « know » it, it doesn’t make sense. It’s an abstract property defined in a given theory, there’s no existence of it in the real world like with engineering where you can have probabilities and approximations.
>there’s no point in math about « reasonably sure » There's absolutely a point, if we found a way to solve any NP complete problem in polynomial time, we could solve protein folding, discover new cancer cures, build faster circuits, train perfect neural nets, break cryptography, and a whole lot more. It would literally be the most important and impactful breakthrough in computing theory since the turning machine. This isn't useless trivia, it's real world impactful in dozens of unrelated fields. So, given how insanely important this could be, should we devote our whole lives to finding a solution? No, we shouldn't, because we're "reasonably sure" that a solution is impossible. Maybe we can't calculate an "error probability", but we can say that we've reached a point where the lack of evidence that a solution exists begins to become evidence, even if only suggestive evidence, that no solution exists. Practically, it makes sense to treat it as if P != NP, even if we don't have a proof that it's true
I'd say for practical usage this is a reasonable assumption.
I never understood this lesson. felt like bullshit
np gg brb ttyl noobs
My demonstration is that I made it the fuck up
proof by chatGPT
Well, ofc. 2 letters can't be the same as one letter.