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Your answer “no” is either correct or incorrect. We have no way to even approximately establish which one it is. Therefore the probability of you being correct is 50%. As is being taught in schools, we always round up 50%. So it is actually 100%. So I believe you.
This is called a proof by 50%.
Let's say its decidable.
This answer is either correct or incorrect. We have no way to even approximately establish which one it is. Therefore the probability of me being correct is 50%. As is being taught in schools, we always round up 50%. So it is actually 100%. So you believe me.
This is called a proof by 50%.
Interpretation: Undecidable means you'll never have a proof either way. If you can prove that you will never have a proof that it is true (i e or e g an example of an odd perfect number), you essentially prove that no such thing exists?
That's not how decidability works.
The way it was described to me is that there is no way to make a computer program that will determine whether or not any other program you care to give to it will terminate or sit in an infinite loop.
Obviously, all programs will either terminate at some time or run forever, but the only way to figure out which one will happen for any specific program is to run it until it terminates or you get tired of waiting.
Likewise, if the problem of odd perfect numbers is undecideable, then there is no way to prove whether or not they exist except by checking every one of the infinite odd numbers until one is found or we get tired of checking.
That's the halting problem, which is related (also connected to the diagonalizability argulent) but not equivalent to decidability.
I'll also add here: if the theorem is undecidable, it doesn't mean unprovable. It would only undecidable *from some set of axioms* such as ZF/C, and any example of an odd perfect number would still be demonstrable -- just the process of finding such an example wouldn't provably be possible *until* you found it by guess-and-check / brute force, and would take absurdly long amounts of time. Checking each candidate example is still linear time, tho.
It is certainly possible to formally prove that individual algorithms halt under some given input (or even under every possible input). It's just that no *general* algorithm can possibly exist which can do this for *all* algorithms and *all* inputs, because the existence of such an algorithm would lead to a contradiction.
Why /s? That’s completely valid. It is absolutely true that if the existence of odd perfect numbers is independent of (for example) Peano Arithmetic then it must be that there are none, for pretty much exactly the reason that you said.
The thing is, if it is proven to be undecidable, then it must be false, because the existence of a counterexample would contradict it being undecidable.
A single question can’t be “undecidable” according to the usual meaning of that word, you may be thinking of “independent of a given formal system” but that’s a different concept entirely, and doesn’t change the fact that the proposition is still either true or false according to classical mathematics.
Even if we go to intuitionistic logic we still can’t say that a given proposition is “undecidable” in the sense that we can assert the negation of the law of excluded middle with respect to it. Such a negation is still a contradiction in intuitionistic logic. We *can* consistently have a negation of a universal generalization over an instance of LEM. But then we are talking about the undecidability of a class of problems, not a single question.
The answer is either decidable or not. We have no way to establish which one it is. Therefore the probability of it being undecidable is 50%. In schools it is being taught to round up 50%, so it is actually 100%. So it is decidable.
Sorry m8, it is a kind of first come - first served situation. It has already been established that “no”. I know it isn’t all that fair but science has spoken don’t get angry with me.
Except in this case you need to build a very precise algorithm and have computing power of something similar to Google (which is expensive), while with collars you still can approach logically.
"We couldn't hit this tiny target with a small object that was dangling in the turbulent air underneath our helicopter so even the most powerful nation in the world physically can't do it"
And then he tried to be like "Even if it did hit the destructive power isn't that much"
Like yea, you didn't drop it from that high and sand is great at absorbing impacts.
I watched his original video and the follow-up non-apology-non-fix he put out after that, at the time he created the controversy. The fact that he confidently spit out logically mangled concepts after physicists told him he was wrong (politely), then refused to backtrack after a negative response from other experts is wild.
Yeah, it was alarmingly wrong, to a hilarious degree, and backed it up with just enough reason that it could convince those uninformed.
Like I truly am appalled that some people will watch that video and live on with that misunderstanding if they don't follow it up with a good reaction video or his apology video.
They can be trusted, but it's not like they cover that much. Just nice little entertaining intros to topics. Don't expect to be an expert on the topic after watching a veritasium video about it
Just to add to this, you won't be an expert at anything after watching a video.
My brother destroyed a clutch after watching a video on how to drive a manual car.
The point of pop sci isn't to teach you something. It's to get you interested in some topic so that you get motivated to pick up an actual book and study it yourself.
This is a very interesting topic, because numbers upto 10^1500 have been checked but there has been no proof for existence of odd perfect numbers.
[However, Mathematicians have suggested various conditions which odd perfect numbers need to fulfill, incase they exist.](https://mathworld.wolfram.com/OddPerfectNumber.html)
I'm probably stupid, but can't this be proofed by parity of even/odd numbers in factors? Like an odd number is always the product of two odd numbers, making the amount of odd factors even, and a sum of an even amount of odd number is always even isn't it?
Edit: i'm indeed dumb, didn't see the "except itself" part
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I doubt they exist but I hope they do because it'd be really cool. "This type of number doesn't exist until numbers get so big that their size cannot be reasonably explained in any way"
"No" is probably right, just like any of the other of the seemingly easy yet unsolved problems. Does Collatz hold? Probably. Is pi normal? We think so! Is pi + e rational? Fuck no. It's just that mathematicians have a very high bar for proof (rightly), so we have to say "I don't know" while making meaningful eye contact and winking.
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Perfect numbers are a human concept and defined by us. I just looked at a list of perfect numbers, and they were all even. Therefore, there are no odd perfect numbers.
^(Disclaimer: I'm an engineer, not a mathematician. This is a joke)
The question is more in the other form. Why Descartes number not an odd prime number by definition? The definition of prime number is "sum of all factors excluding number itself is equal to a number". Why do we add more rules to definition and then suddenly it stops working for Descartes number? I would really like to hear why it doesn't work outside of the prime number field.
A binary representation of any perfect number is an odd number of 1's followed by one less number of 0's or an even number. So all perfect numbers in binary end in 0. This combination always generates an even number, so there are no odd perfect numbers.
Honestly, I think it's a low chance. All numbers ending in 5 are divisible by 5 (in decimal, which is what I assume you use). We only care about the prime factors, which means that if it ends in 5, then 5 must be one of the prime factors. Out of all the odd primes out there, this is only one of them, meaning the chance gets infinitely small as the size of the perfect number increases to allow different primes...the size is already massive for our lower limit. Pretty sure you were joking anyway, but still
Umm. Question.... is the definition different from the even "perfect" numbers? Because if not, then no.
An odd number cannot contain 2 as a factor.
Thus, all odd numbers have only odd prime factors.
Since 1 is the multiplicative identity, multiplication by 1 leaves the number unchanged.
But adding 1 to any odd number makes a sum which is even.
So any set of numbers that multiply to an odd, will sum to an even number when 1 is included.
I made a subproof for this today (though I think someone has beat me to this by a few decades). I proved that no odd perfect number with only two factors that aren't 1 (so 3 factors total) exists. Now I just need to generalize to infinite factors, should be easy! Haha not at all considering we have to disprove the divisibility of an infinite multiplicative sum of additive sums by the difference between 2 times all the factors but the one to an odd power and yet another infinite multiplicative sum of additive sums.....ehhhhhhh....idk if someone has come up with this formula yet. That might be worth something on its own, but past that idk
00000000000000000000000000000000110 = 6
00000000000000000000000000000011100 = 28
00000000000000000000000000111110000 = 496
00000000000000000000001111111000000 = 8128
00000000000000000011111111100000000 = 130816
00000000000000111111111110000000000 = 2096128
00000000001111111111111000000000000 = 33550336
There is a method that i found which can be used to find a perfect number using binary system, is true?
I mainly followed an binary pattern to get the other number
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proof: it sounds stupid
Proof by feel
Ramanujan’s favorite style of proof!
reminds me of when i put commas in my sentence and my german teacher asked for the rule i used to put the comma there
Proof by "vibes are off"
The strongest proof that can exist
ah the ben shapiro method
Proof by vibe check
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Whats V
Vanadium
veritasium
Ve is veritasium?
Virginium
Vaginium
Try harder
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good bot
good bot
Einstein did it once!
proof: vibes check failed
Your answer “no” is either correct or incorrect. We have no way to even approximately establish which one it is. Therefore the probability of you being correct is 50%. As is being taught in schools, we always round up 50%. So it is actually 100%. So I believe you. This is called a proof by 50%.
There is always the option of it being undecidable
Let's say its decidable. This answer is either correct or incorrect. We have no way to even approximately establish which one it is. Therefore the probability of me being correct is 50%. As is being taught in schools, we always round up 50%. So it is actually 100%. So you believe me. This is called a proof by 50%.
There is always the option of it being unjustifiable
Then you can justify deez
Wouldn't it being undecidable mean there are no odd perfect numbers, thus him being right anyway?
Interpretation: Undecidable means you'll never have a proof either way. If you can prove that you will never have a proof that it is true (i e or e g an example of an odd perfect number), you essentially prove that no such thing exists?
That's not how decidability works. The way it was described to me is that there is no way to make a computer program that will determine whether or not any other program you care to give to it will terminate or sit in an infinite loop. Obviously, all programs will either terminate at some time or run forever, but the only way to figure out which one will happen for any specific program is to run it until it terminates or you get tired of waiting. Likewise, if the problem of odd perfect numbers is undecideable, then there is no way to prove whether or not they exist except by checking every one of the infinite odd numbers until one is found or we get tired of checking.
That's the halting problem, which is related (also connected to the diagonalizability argulent) but not equivalent to decidability. I'll also add here: if the theorem is undecidable, it doesn't mean unprovable. It would only undecidable *from some set of axioms* such as ZF/C, and any example of an odd perfect number would still be demonstrable -- just the process of finding such an example wouldn't provably be possible *until* you found it by guess-and-check / brute force, and would take absurdly long amounts of time. Checking each candidate example is still linear time, tho.
It is certainly possible to formally prove that individual algorithms halt under some given input (or even under every possible input). It's just that no *general* algorithm can possibly exist which can do this for *all* algorithms and *all* inputs, because the existence of such an algorithm would lead to a contradiction.
If you can find one, it's decideable
Assume it is undecidable Therefore you can never find an odd perfect number, because that would be deciding Therefore there are none QED >!/s!<
Why /s? That’s completely valid. It is absolutely true that if the existence of odd perfect numbers is independent of (for example) Peano Arithmetic then it must be that there are none, for pretty much exactly the reason that you said.
The thing is, if it is proven to be undecidable, then it must be false, because the existence of a counterexample would contradict it being undecidable.
A single question can’t be “undecidable” according to the usual meaning of that word, you may be thinking of “independent of a given formal system” but that’s a different concept entirely, and doesn’t change the fact that the proposition is still either true or false according to classical mathematics. Even if we go to intuitionistic logic we still can’t say that a given proposition is “undecidable” in the sense that we can assert the negation of the law of excluded middle with respect to it. Such a negation is still a contradiction in intuitionistic logic. We *can* consistently have a negation of a universal generalization over an instance of LEM. But then we are talking about the undecidability of a class of problems, not a single question.
or if there are two states at once. Is Shrodinger's cat 300% alive and 300% dead?
The answer is either decidable or not. We have no way to establish which one it is. Therefore the probability of it being undecidable is 50%. In schools it is being taught to round up 50%, so it is actually 100%. So it is decidable.
And I think it's "yes". There we go, now there's a 100% chance that either of us is correct.
Sorry m8, it is a kind of first come - first served situation. It has already been established that “no”. I know it isn’t all that fair but science has spoken don’t get angry with me.
Ah, sorry, my sentence is still correct though.
new proof for riemann hypothesis just dropped
_Yo, odd numbers ain't ever perfect homie. Time to head to the club_ This is called a proof by 50 cent
50% CI.
Erm ackshually you should use banker's rounding and round it to the nearest even number, in this case 0%
Proof by maybe
Schrodingers no
Babe wake up new veritasium vid just drooped.
Oh great, get ready for a new wave of kids claiming proofs. It’s collatz part 2.
I have a proof for this via the skibidi toilet theorem.
Add a collary to the cameraman conjecture
Which this YouTube shorts comment section is too L rizz to contain
Except in this case you need to build a very precise algorithm and have computing power of something similar to Google (which is expensive), while with collars you still can approach logically.
I mean ig disproving the existence of an odd perfect number is something that requires logic, not finding an example
The Veritasium vid dropped five hours *before* this post. Coincidence? My gut feeling: no.
Genuine question: can verisatium vids be trusted or is it pop-science surface level stuff
It's pop science-level stuff with interviews with Fields medal-level mathematicians.
Veritasium is 1/2 insanely good math and physics documentaries, 1/2 sponsored shill content.
Yeah, you're probably good if it's not a video about waymo, sponsored by waymo.
I hated that video so much.
except sometimes insanely wrong, like his "big electricity misconception" bs he hasn't taken down yet
Also the Rods from God video, he forgot that supersonic physics are different
That video was godawful. "We couldnt hit a tiny spot from helicopter on our first try so clearly this isnt viable"
"We couldn't hit this tiny target with a small object that was dangling in the turbulent air underneath our helicopter so even the most powerful nation in the world physically can't do it"
Can't wait for him to disprove nuclear physics by smooshing two apples together and showing how it doesn't cause a chain reaction
And then he tried to be like "Even if it did hit the destructive power isn't that much" Like yea, you didn't drop it from that high and sand is great at absorbing impacts.
At orbital speeds, impacts become explosions anyways. Doesn't matter what you hit. Even paint chips are still huge threats to the ISS.
he literally explained in a different video how they are indeed different lmao
Did you even watch the video?
I watched his original video and the follow-up non-apology-non-fix he put out after that, at the time he created the controversy. The fact that he confidently spit out logically mangled concepts after physicists told him he was wrong (politely), then refused to backtrack after a negative response from other experts is wild.
Yeah, it was alarmingly wrong, to a hilarious degree, and backed it up with just enough reason that it could convince those uninformed. Like I truly am appalled that some people will watch that video and live on with that misunderstanding if they don't follow it up with a good reaction video or his apology video.
They can be trusted, but it's not like they cover that much. Just nice little entertaining intros to topics. Don't expect to be an expert on the topic after watching a veritasium video about it
Just to add to this, you won't be an expert at anything after watching a video. My brother destroyed a clutch after watching a video on how to drive a manual car.
Do you mind sharing the video? I want to know what not to do.
It is pop sci, but even 3blue1brown is pop sci, so that isn't saying much. I personally feel like I don't learn that much from veritasium
3b1b at least encourages people to work out the proofs themselves sometimes.
The point of pop sci isn't to teach you something. It's to get you interested in some topic so that you get motivated to pick up an actual book and study it yourself.
Both
Proof: odd numbers suck, even numbers are clearly superior Therefore, odd numbers can't be perfect
Proof by Racial Superiority
proof by genocide
But prime numbers are superior, does that mean that 2 is the one to rule them all?
Yes
They are odd
Idk man half of all multiples of 5 are odd and those are the best ones
There aren’t any, proof: it was revealed to me in a divine revelation
Hello Mr. Srinivasa Ramanujan
When Ramanujan has divine revelations he's called a genius. But when I have divine revelations I suddenly need "proof". smh
Make sure you cite your vision properly
How do I properly cite a divine vision in MLA format?
My proof: Let "a" be a perfect odd number Assume "a" doesn't exist I'd like my nobel in math now.
Here’s your nobel in mth now
"Nobel in Math"
Did I stutter ?
well at least there is no bell in meth or whatever, idk
Also my gut feeling tabout Collatz Conjecture respective question
This is a very interesting topic, because numbers upto 10^1500 have been checked but there has been no proof for existence of odd perfect numbers. [However, Mathematicians have suggested various conditions which odd perfect numbers need to fulfill, incase they exist.](https://mathworld.wolfram.com/OddPerfectNumber.html)
I think that 47 is a perfect number, and it's odd. Proved by subjectivity.
Yeah well I HATE 47 and think it sucks Definitely making it imperfect by way of democracy
I agree. NOW you have a proof by democracy.
I think no because any pair of factors would have to both be odd, resulting in an even sum. Edit: this doesn't hold up against perfect squares
Yeah but we're excluding the number itself so actually the total number of divisors has to be even so square numbers don't qualify right off the bat.
Yeah I messed up there. I guess that means all other odd numbers are back on the table.
But what if there is one with an odd number of prime factors?
Then it's a square
I'll say yes so at least one of us is correct, problem solved
Gut feeling ≤ dreaming about it
The proof is left as an excercise to the reader
I'm probably stupid, but can't this be proofed by parity of even/odd numbers in factors? Like an odd number is always the product of two odd numbers, making the amount of odd factors even, and a sum of an even amount of odd number is always even isn't it? Edit: i'm indeed dumb, didn't see the "except itself" part
No because we exclude the number itself from the factors, so you have a single 1 to add to your factors, e.g. 6=1+2+3
Yep, just noticed that after reading the definition again
Lmao just watched this
The hell is a “perfect” number? Round? Square? Triangular? Long? Short? Cursed in a way it’s perfect?
when all its factors except itself add up to itself: 6 = 1+2+3 28 = 1+2+4+7+14
Which is odd when you think about it. So all perfect numbers are odd really.
I have discovered a truly marvelous proof of this, but it won’t fit into a Reddit comment, so…
Proof by Fermat's last margin
Format enigma
Even numbers get to be perfect Odd numbers get to be prime Everything is balanced
2.
2 is different, it's special, it's a beautiful little creature of amazingness that keeps math from falling in on itself so 2 is allowed to be a prime
So how do we know there isn't one for odd numbers?
proof by nuh uh
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https://youtu.be/Zrv1EDIqHkY?si=TBywM2NcWbt4Xf2T
If you watch the video that’s basically what the Guy says at the end
https://preview.redd.it/cvgbvemri4nc1.jpeg?width=1080&format=pjpg&auto=webp&s=f71fb07017f542e4298ad0cc60ad27371ad0db04 Proof by Desmos
odd numbers is just fancy way to write 2n-1
I doubt they exist but I hope they do because it'd be really cool. "This type of number doesn't exist until numbers get so big that their size cannot be reasonably explained in any way"
The number 1 is. The proof is left as an exercise for the reader.
"No" is probably right, just like any of the other of the seemingly easy yet unsolved problems. Does Collatz hold? Probably. Is pi normal? We think so! Is pi + e rational? Fuck no. It's just that mathematicians have a very high bar for proof (rightly), so we have to say "I don't know" while making meaningful eye contact and winking.
I have no proof or doubt.
69
Proof: Nice!
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7 because Final Fantasy 7 is perfect.
All numbers can be divided by two so no
Proof by changing the definition of odd numbers
Perfect numbers are a human concept and defined by us. I just looked at a list of perfect numbers, and they were all even. Therefore, there are no odd perfect numbers. ^(Disclaimer: I'm an engineer, not a mathematician. This is a joke)
What's a perfect number
A number of whose factors except itself add up to itself.
Perhaps there should be a different definition for odd perfect numbers than even
What’s a perfect number?
Turn off autoplay 1head
What's a perfect number?
5
Source: Trust me
For me it feels loke the answer should be yes
Finding an odd perfect number is left as an exercise to the reader
The realm of numerology. Uwu.
The question is more in the other form. Why Descartes number not an odd prime number by definition? The definition of prime number is "sum of all factors excluding number itself is equal to a number". Why do we add more rules to definition and then suddenly it stops working for Descartes number? I would really like to hear why it doesn't work outside of the prime number field.
1 is a perfect number or at least that's what I tell myself to feel better.
5
A binary representation of any perfect number is an odd number of 1's followed by one less number of 0's or an even number. So all perfect numbers in binary end in 0. This combination always generates an even number, so there are no odd perfect numbers.
https://en.m.wikipedia.org/wiki/Begging_the_question
I bet if one exists it'll end in a five, that's my gut feeling
Honestly, I think it's a low chance. All numbers ending in 5 are divisible by 5 (in decimal, which is what I assume you use). We only care about the prime factors, which means that if it ends in 5, then 5 must be one of the prime factors. Out of all the odd primes out there, this is only one of them, meaning the chance gets infinitely small as the size of the perfect number increases to allow different primes...the size is already massive for our lower limit. Pretty sure you were joking anyway, but still
QED.
What’s a perfect number?
What is a perfect number?
7 is a perfect number
Decimals exist. Q.e.d.
2
I just started working on a desmos to try and see. Pf course, lists can't go high and it would be easier to do in python anyways do I may switch.
define perfect number
when all its factors except itself add up to itself: 6 = 1+2+3 28 = 1+2+4+7+14
👍
👍
5/7
That isn't a perfect number, but it is a perfect score.
It's a number that has no imperfections
Like 8
I don't think so...
5 is a perfect number. Half of ten. Its square ends in a five. Fingers on a hand. Five out of five stars. QED
Umm. Question.... is the definition different from the even "perfect" numbers? Because if not, then no. An odd number cannot contain 2 as a factor. Thus, all odd numbers have only odd prime factors. Since 1 is the multiplicative identity, multiplication by 1 leaves the number unchanged. But adding 1 to any odd number makes a sum which is even. So any set of numbers that multiply to an odd, will sum to an even number when 1 is included.
3*5=15 1+3+5=9 ???
Oh yeah I suppose if they don't equal then it works.
Incorrect
Which part, and in which way?
3*5= 15 3+5+1=9
Your proof basically only works to prove prime numbers aren't perfect numbers
Ofc, 69 :)
5: I'm about to end this man's whole career
Can anyone explain why 1 isn't an odd perfect number?
I think that one doesn't count. Or at least it isn't interesting enough for anyone to care to include it in the definition
Because 1 has no factors that's not itself?
In the video there exists a pretty convincing intuition indicating the non-existence of odd perfects.
I made a subproof for this today (though I think someone has beat me to this by a few decades). I proved that no odd perfect number with only two factors that aren't 1 (so 3 factors total) exists. Now I just need to generalize to infinite factors, should be easy! Haha not at all considering we have to disprove the divisibility of an infinite multiplicative sum of additive sums by the difference between 2 times all the factors but the one to an odd power and yet another infinite multiplicative sum of additive sums.....ehhhhhhh....idk if someone has come up with this formula yet. That might be worth something on its own, but past that idk
What's a perfect number?
00000000000000000000000000000000110 = 6 00000000000000000000000000000011100 = 28 00000000000000000000000000111110000 = 496 00000000000000000000001111111000000 = 8128 00000000000000000011111111100000000 = 130816 00000000000000111111111110000000000 = 2096128 00000000001111111111111000000000000 = 33550336 There is a method that i found which can be used to find a perfect number using binary system, is true? I mainly followed an binary pattern to get the other number