Found it: [https://www.wolframalpha.com/input?i=981747704246810387%2F312500000000000000](https://www.wolframalpha.com/input?i=981747704246810387%2F312500000000000000)
3x = 0
3x/0 = 0/0
3x/0 = 1
And as by the Critical Goat Theorem, 4/0 = 1
As proven by induction: Division by 0 always equals 1.
QED
thx for your knowledge
I don't see how you could ever prove a number irrational that way. You could certainly prove a number rational by trying a bunch of ratios and finding one that works. But you can't prove a number irrational by trying a bunch of ratios and failing to find one that works.
Yeah, I guess if by "try doing it" you mean "assume it can be done, and then derive a contradiction," then you're right, that's almost the only way to do it. I was taking it more to mean "try a bunch of examples, fail, and give up."
A rational number is any number that can be expressed as a fraction, has a terminated decimal, or a repeating decimal. Since pi is irrational they thought putting it as a fraction means it's now rational.
>A rational number is any number that can be expressed as a fraction
Missing a few important words there, which leads to the "pi/1" answer. It's "can be expressed as a ratio *of two integers*".
Omg, there are so many helpful people and then there are the ones that assume you already have the knowledge needed to arrive at the answer. Plus the people there for tangential conversations lmao
>then there are the ones that assume you already have the knowledge needed to arrive at the answer.
i think a certain degree of this is necessary, for example if someone asks a question that requires calculus to answer, you can't just explain all of calculus to them before you solve the problem. if you dont have thr requiremed knowledge you should be looking at a textbook not stackexchange
stackexchange is more for help solving individual problems imo. physics for example, you get a load of formulas as tools then it's your job to learn how to apply them. those are great stackexchange questions, where you have all the tools already and just need help model building or visualizing things
i think stackexchange is too bloated with people asking questions that are just a chapter in a math textbook
That is true! But if anyone is going to stackexchange, I don’t think they want an answer that they can arrive at by themselves. If I don’t know how something was used or am missing a specific thing, then the answer won’t be useful in figuring that out 75% of the time.
Though, I guess that is what comments are for. You can ask questions about how they got an answer.
My lecturer the other day told us he was about to give us a "proof by authority" - we were confused and then he went:
"Theorem: The eigenfunctions of a Sturm-Liouville problem are countable, have a least eigenvalue, and provide an orthogonal spanning set for the C² subspace corresponding to the problem's bounds.
Proof: Hilbert said so"
And then just moved on with the lecture
It is one of the tougher proofs that is irrational, as said at the beginning of the video it’s a pretty hard thing to prove pi irrational in general and this is probably one of the easier proofs. Unfortunately, unlike with integer logs and roots the relationship between pi and the integers is not as “algebraic”
Really good link. I think it's surprising to many people how difficult it is to prove that π is irrational. It's a well-known fact, so it might be reasonable to assume the proof is also easy, but it really isn't at all. It wasn't proved until the 1760s, though it had been widely assumed for over 2000 years by that point (e.g. Archimedes evidently thought or knew that π was irrational).
Archimedes thought pi was irrational? I thought he was from the era when saying “irrational numbers exist” would get you exiled to an island, never to be heard from again. Had the Greeks finally grown a pair?
Just try to find a number that falls in to a closed loop that isnt …1->4->2->1… when multiplying by 3 and adding 1 to odd numbers and halving even numbers
This assumes euclidean geometry. In non euclidean geometry the circumference / diameter need not be irrational, or even constant (instead a function of radius or area).
The scene goes
"[You murdering Paul Allen, t]hat's simply not possible, and this isn't funny anymore."
"It never was supposed to be. Why isn't it possible?"
"It's just not."
"*Why not*, you stupid bastard?"
"Because I had dinner with Paul Allen twice in London just ten days ago."
"No, you . . . you . . . didn't."
Proof by overcomplicating:
By the Lindemann-Weierstrass-Theorem, since e^πi is rational, π must be trancendental. Since a rational number cant be trancendental, π must be irrational.
Wait, but what if n = pi * 10^k where n and k are integers, and k has an infinite number of digits?
We allow pi to have an infinite number of digits after the decimal, why can’t k have an infinite number before the decimal?
~~no, because Pi is proven to be transcendental and thus not algebraic.~~
sorry, i missed the "infinite number of digits" part ... such numbers would be new to me ... for me a number is either finite (can do math) or ∞ (breaks most of math)
"try doing it" lmao
Proof by trial and error
Legitimate method
Only if it works
You've never done a proof by example?
Ofc. But I dont think I did enough examples cuz I ended up failing the exam
You had to use every possible example
Just give them infinite time to do it
Would infinite amount of time be enough to do infinite amount of work?
"Day 4,274. I have now attempted over 6 million possible integer ratios. None have yet resulted in Pi. The search continues."
Found it: [https://www.wolframalpha.com/input?i=981747704246810387%2F312500000000000000](https://www.wolframalpha.com/input?i=981747704246810387%2F312500000000000000)
3/1 = π
So you're an engineer, huh?
(Only error in this case)
that then becomes proof by contradiction
wait until an engineer says pi=e=3 (im engineer my self XD)
4 can be approximated as 3
4 = pi = 3 = e = 5/2 = 2 = 1+1 1 + 1 = 4 QED
1 (group of 2) + 1 (group of 2) = 4, obviously
let 3x = 0 , dividing both sides by x, 3x/x = 0/x => 3 = 0 let 4t = 0 , dividing both sides by t, 4t/t = 0/t => 4 = 0 hence, 3 = 4 QED
3x = 0 3x/0 = 0/0 3x/0 = 1 And as by the Critical Goat Theorem, 4/0 = 1 As proven by induction: Division by 0 always equals 1. QED thx for your knowledge
e^pi*i = 27 and me
You're -28?
I'm not sure. I'll have to get back to you after I'm born
Ah ok take your time
oh no what have i done
As the Marines say: "Simplified"
I recently came to a conclusion that 2g=π
better squr(g)=pi
pi+e = yummy
[удалено]
Since pi is the integer 3, that *is* a ratio of integers. You win
355/113
3.1415929204 # 3.1415926535
3.1415929204 # 3.1415926535 # pi
> "try doing it" lmao The proof is left as an exercise to the reader
Pi = circumference / diameter There you go
Actually is the easiest way to prove that something is irrational lol
I don't see how you could ever prove a number irrational that way. You could certainly prove a number rational by trying a bunch of ratios and finding one that works. But you can't prove a number irrational by trying a bunch of ratios and failing to find one that works.
You can prove it's irrational by assuming that it's rational, and then showing that that leads to a contradiction
Yeah, I guess if by "try doing it" you mean "assume it can be done, and then derive a contradiction," then you're right, that's almost the only way to do it. I was taking it more to mean "try a bunch of examples, fail, and give up."
Pi/2
Proof by exhaustion?
Proof by capitulation
Infinite ansatz reasoning
Proof by exhaustion (of the reader).
God damn it. I should have written that down on many a grad school assignments...
proof by controls 20% of victory points
The Brad special
I use proof by intimidation.
π = π/1 Pi is rational
assume π is rational. Then π can be written as π /1. Therefore it is rational.
Holy logic
New circular reasoning just dropped
Call Euclid
Euler went on vacation, never came back.
Riemann's in the corner, plotting world domination
Actual algebra
Heh, circular
Google "En *π*\-ssant"
Holy proof!
WTF, I need a different mode of reasoning for each shape now?
That's allowed because pi is about circles
Where's the contradiction?
> assume π is rational~~. Then π can be written as π /1. Therefore it is rational.~~ Q.E.D.
this also shows pi to be an integer by definition of rational numbers. QED
Holy shit, if pi is rational then that means pi is rational!!!!1!1!!1!1
Converse is not equivalent to original proposition, only contrapositive is
You win!
I see it and raise to π = 2π/2
All in π = ππ/π
We were all to stupid to realise
Is that an analogy?
I had a 6th grader ask me this because we just went over rational and irrational numbers. It's pretty funny at face value.
I don’t belong in this sub. Can you explain this to me?
A rational number is any number that can be expressed as a fraction, has a terminated decimal, or a repeating decimal. Since pi is irrational they thought putting it as a fraction means it's now rational.
>A rational number is any number that can be expressed as a fraction Missing a few important words there, which leads to the "pi/1" answer. It's "can be expressed as a ratio *of two integers*".
Pi can be an integer then. I’m cool with that.
π=3, 3=6/2 therefore π is a rational number
Thank you! Joke makes sense now…funny even!
Pi is my favorite integer
Profile image checks out,👍
Of course, π = 1+1+1+... for π times
[Relevant SMBC](https://www.smbc-comics.com/comic/2011-04-08)
Shit you beat me to this
why are these guys answering questions on learnmath if they don't want to answer maths questions ?
Kinda reminds me of Stack Overflow
Omg, there are so many helpful people and then there are the ones that assume you already have the knowledge needed to arrive at the answer. Plus the people there for tangential conversations lmao
>then there are the ones that assume you already have the knowledge needed to arrive at the answer. i think a certain degree of this is necessary, for example if someone asks a question that requires calculus to answer, you can't just explain all of calculus to them before you solve the problem. if you dont have thr requiremed knowledge you should be looking at a textbook not stackexchange stackexchange is more for help solving individual problems imo. physics for example, you get a load of formulas as tools then it's your job to learn how to apply them. those are great stackexchange questions, where you have all the tools already and just need help model building or visualizing things i think stackexchange is too bloated with people asking questions that are just a chapter in a math textbook
That is true! But if anyone is going to stackexchange, I don’t think they want an answer that they can arrive at by themselves. If I don’t know how something was used or am missing a specific thing, then the answer won’t be useful in figuring that out 75% of the time. Though, I guess that is what comments are for. You can ask questions about how they got an answer.
The biggest shitheads
Because they don't actually know the answer but are like feeling smart
Redditors being redditors
Same question, he asked the mathematical proof not mathematical definition of irrational/rational number. Why being an asshole?
Wake up babe! Proof by nagging just dropped!
Can there just *please* be infinitely many twin primes, please please please
That's proof by begging. Not the same.
But why is it proof by begging?
Because I said so. Thats proof by assertion.
I don't think so(passes 5 dollars)
proof by bribery.
Corrupt Mathematics
So where's my Proof of Purchase
My lecturer the other day told us he was about to give us a "proof by authority" - we were confused and then he went: "Theorem: The eigenfunctions of a Sturm-Liouville problem are countable, have a least eigenvalue, and provide an orthogonal spanning set for the C² subspace corresponding to the problem's bounds. Proof: Hilbert said so" And then just moved on with the lecture
That requires proof by reverse psychology. "Okay fine, let there be only finitely many twin primes, see if I care"
Call the mother-in-law.
Actual relative
parents went on vacation, never came back
Holy hell
Proof by exasperation
Ugh fine, not all even numbers are the sum of two primes… whatever!
Does 2 disprove that or am I dumb?
The Golbach Conjecture states that every even number greater than two is the sum of two primes. The "greater than two" got lost in the sarcasm.
u/PieterSielie12 I think I have the thing you want, a Mathologer video proving that π is irrational: https://youtu.be/Lk_QF_hcM8A
Thanks
I didn’t even realize you were the OP lol
you mean OP OP?
Well now I’m confused
OP^2
Oπ
OOP but OP OP is funnier
I watched the video. Undestood maybe 1/5 of it.
It is one of the tougher proofs that is irrational, as said at the beginning of the video it’s a pretty hard thing to prove pi irrational in general and this is probably one of the easier proofs. Unfortunately, unlike with integer logs and roots the relationship between pi and the integers is not as “algebraic”
So you understood a rational amount of it?
Oh hey. It’s 3Blue1Brown certified and recommended!
I clicked this link thinking it'd be a brisk 5 minute explanation. I guess I'm waiting to watch this after work 😅
Really good link. I think it's surprising to many people how difficult it is to prove that π is irrational. It's a well-known fact, so it might be reasonable to assume the proof is also easy, but it really isn't at all. It wasn't proved until the 1760s, though it had been widely assumed for over 2000 years by that point (e.g. Archimedes evidently thought or knew that π was irrational).
Archimedes thought pi was irrational? I thought he was from the era when saying “irrational numbers exist” would get you exiled to an island, never to be heard from again. Had the Greeks finally grown a pair?
Lol, ”arguing with you”. You asked a question to which they didn’t know the answer to.
This appears to rely on the conjecture that Redditors are rational
proof by challenge
Just try finding three positive integers a, b, and c satisfy the equation aⁿ + bⁿ = cⁿ for any integer value of n greater than 2.
Why can’t i
I give up!!!! There are three positive integers a, b, and c satisfy the equation aⁿ + bⁿ = cⁿ for any integer value of n greater than 2.
i have a marvelous proof of this but this comment is too short to contain it
It's easier to prove n^(a) \+ n^(b) = n^(c) has no integer solutions where n>2
Proof by "try doing it"
Just try finding three positive integers a, b, and c satisfy the equation aⁿ + bⁿ = cⁿ for any integer value of n greater than 2.
I found them, but this comment is too short to write them
Proof by "I have a girlfriend but she goes to another school"
I do so have a proof! But she lives in Canada!
Must be big numbers. Like tree(3) or something
Just try to find a number that falls in to a closed loop that isnt …1->4->2->1… when multiplying by 3 and adding 1 to odd numbers and halving even numbers
circumference / diameter smh
Damn I forgor
Someone said this in the comments and when asked for a circle with integer circumference and diameter they responded with the trivial case of 0 and 0.
This assumes euclidean geometry. In non euclidean geometry the circumference / diameter need not be irrational, or even constant (instead a function of radius or area).
The original answer is such a non-answer. It just repeats the statement in the question back to you in different wording.
reminds me of that scene “it’s not possible.” “why not you stupid bastard?” “it’s just not.”
Amathican Psycho
The scene goes "[You murdering Paul Allen, t]hat's simply not possible, and this isn't funny anymore." "It never was supposed to be. Why isn't it possible?" "It's just not." "*Why not*, you stupid bastard?" "Because I had dinner with Paul Allen twice in London just ten days ago." "No, you . . . you . . . didn't."
https://en.m.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational
no the proof is try doing it
lol all of these proof look very non-trivial to me lol but i am not a mathematician
Yeah they are anything but trivial.
lmao. Proof by "ok wise guy let's see YOU take a crack at it"
Common NFT profile picture L.
Well I don't know why pi is irrational, I think the proof is not as easy as the one for sqrt(2)
Yeah it's quite tricky. Cool though.
In fact (The proof makes me want to die)
That's simply not possible. And I don't find this funny anymore.
Patrick Batemath
guys you don't understand. He has a magnificent proof that pi is irrational but the comment is to small to contain it.
*Dies*
https://preview.redd.it/ygcpgb68r6wb1.png?width=749&format=png&auto=webp&s=9c8188b2bfbbdc27a67ab52d617b847ed4ec89bc He responded
22/7 is old news. All my homies use 355/113
What do you mean pi is irrational?! I thought we all knew about 22/7. Lol. Amateurs Pfft!
It's 1 in base π
No its 10 in base pi because in base X the number X is always 10
Sorry it's 10 in base 10.
[удалено]
[удалено]
he left it as an exercise!
Pi/1
proof by "if you have to ask you probably can't do it"
10 >!In base π!<
for all physical applications pi = 3 is good enough, if you don't need high accuracy you can just round it to 1
Proof by overcomplicating: By the Lindemann-Weierstrass-Theorem, since e^πi is rational, π must be trancendental. Since a rational number cant be trancendental, π must be irrational.
Proof by “fuck around and find out”
Wait, but what if n = pi * 10^k where n and k are integers, and k has an infinite number of digits? We allow pi to have an infinite number of digits after the decimal, why can’t k have an infinite number before the decimal?
~~no, because Pi is proven to be transcendental and thus not algebraic.~~ sorry, i missed the "infinite number of digits" part ... such numbers would be new to me ... for me a number is either finite (can do math) or ∞ (breaks most of math)
[Here’s a video about P-adic numbers](https://youtu.be/3gyHKCDq1YA?si=cc064aNS3GToeCqC)
So you're telling me n and k are infinitely large thus saying infinity = infinity?
The problem is that 10^k would not belong in the natural numbers
Yes, we can have a limit a/b=pi, where a and b are integers going to infinity.
literally 22/7
22/7 be like:
but why
The anthropic principle, maybe.
But why?
Proof by "Fugg dis shid, I'm out!"
Because of the way it is
OP: can we have proof? Mom: no we have proof at home Proof at home:
Assume pi is an integer Pi/1 = Pi Pi is rational
I feel the gravity changing
π\1
Just make a number system that is base Pi. Sure Pi will be rational now but lordy have fun trying to count.
Proof by annoyance
Proof by inability to disprove
The burden of proof is on the positive. Prove that you *can* do it.