The Four Colour "theorem" is proved [spoiler]not disproved you pussy fart[spoiler] by using computer configuration.
REEEEEEEE
>>8091261
Graph theory being pure is a meme.
Math is ALL applied, there is no pure math; only people who can DO math and those who can only teach it.
The summation of 1/n does not converge, but diverge.
>every injection has a left inverse
>but a surjection need not have a right inverse
Since the axiom of extensionality is part of ZF, this implicates anyone using ZF set theory without C.
>>8091278
it would trigger me more if it converged.
>>8091278
The summation converges but the power series diverges.
>>8091288
You should use epi and mono if you want nice duality
>>8091261
Lel are you a French fag who listened to a Henry de Lesquen interview ?
>>8091278
this desu. I can't accept it to this day.
>>8091338
Je vois pas la rapport, source demandée
>>8091278
Wait what? The term approaches 0, how come?
>>8091395
Look up proof for harmonic series. The term does go to zero but the summation diverges very slowly, similar to an ln series.
>>8091398
>ln
Now I feel retarded, that was way too obvious.
Fuck
>>8091395
After understanding that, here's a more slowly diverging series:
https://en.wikipedia.org/wiki/Divergence_of_the_sum_of_the_reciprocals_of_the_primes
>>8091402
No concerns, I am currently going through an infinite series class so it's fresh in my mind.
>>8091338
Who the hell is Henry de Lesquen? Im just a /vp/ fag who is interested in math, thats all.
I'm just triggered that they gave up on finding the proof for the Four Colour Conjecture and resorting to 'proof by exhaustion' method. That is just bullshit imo.
That is just an insult to all the greasy sweat of previous mathematician in tackling this conjecture.
Can any of you senpai please convince me that this method is acceptable?
[spoiler]I've never fail so hard with black text in my life[/spoiler]
>>8091743
People didn't give up, they just still haven't found an alternative to the computational brute force approach.
It's acceptable because there's no better option.
Why e^(j*pi) + 1 = 0 is some magic relation that autists orgasm about, however no one mentions e^(j*0) - 1 = 0 is the same thing
>>8091757
I get it there are no other alternative. But that doesnt mean that we can close the book and say "Yup, our job is done. We successfully turn a conjecture into a theorem. See you butthurt mathematician on the flip side, pussy fart".
The fact that some conjecture such as Kepler Conjecture is proved by computer configuration soften my boner.
Unsolved math problem need to be solved in a diligent way, not a brute force way...
Pic related is how I imagined the two parties of mathematician in regarding the Four Colour 'Theorem' announcement ceremony.
>>8091853
A theorem is just something that can be proved.
Most people are able to recognize/live with the difference of knowing whether something is true or false and knowing why it is that way.
>>8091261
The Four Colour Theorem is Mathematics and not Computer Science. I do think such work is more technological related. I print my proof documents with the computer. The intuition to the problem is likely the computer's rather than your own. I don't think you will be given credit for solving an original and global problem only with computer systems. It is also not possible - that is, the Mathematician and Computer Scientist are not the same individual. For example, Grigori Perelman's solution to the Poincare Conjecture was incorrect because he presented computer results. I solved it in my head without a computer. 1 not 0. Also, use of computers to solve Mathematics problems would not provide an original proof, answer, or solution. The computer is more of a printer and byway instrument. In short, one is not required to own a computer to solve an original and global Mathematics problem - only to post the solution and proof to such Mathematics problem.
[email protected]
>>8091781
you could replace e by any real number whatsoever in your second equation, you braindamaged shitlord.
also,
>j for sqrt(-1)
lel
on a somewhat related note, though, I also think exp(2*pi*i) = 1 is more sensible. Why would you only go round half a circle?
>>8091919
I completely agree with your somewhat related note, except that I'm a tau-fag because you might as well deal with a unit of revolution and use familiar fractions on it.
And I hate exp() as a notation. But that's my somewhat related.
>>8091870
>>8091904
>>8091757
I really appreciate you senpai feedback, but this is getting way too philosophical. I dont think I can change my mind regarding the Four Color Theorem.
This is a thread where we express our rage, butthurt, autistic critisms towards math. Appreciate if you guys keep complaining
>>8091743
The exhaustion method is a legitimate method. Do you even math bro?
>>8091976
I agree with you, but now that absurd exhaustion is becoming possible, someone has to ask when less exhaustion and more reduction of cases should be striven for.
Godel Incompleteness Theorem really grind Prof Hilbert gear, and many others' gear.
"We dont know, and we wont know"
How can we trust others if we cant even trust the axiom?
>>8091976
>>8092004
>>8091976
Senpai, method of exhaustion is only acceptable if there is CONFIRMED finite amount of variable and step. But what about an ARBITRARY finite variable and step? Or infinite variable and step?
It too unsettling for a mathematician standard. Math is build on a hard solid evidence, not unsettling one.
>Four Color Theorem
Get with the times gramps
http://www.i-programmer.info/news/112-theory/9718-a-mathematical-proof-takes-200-terabytes-to-state.html
>>8092033
You still have to prove that all of the cases you considered were enough to prove the theorem.
>>8092033
What did you just take your intro proofs class? Everyone here knows that to apply exhaustion you must be able to exhaust all cases, meaning they aren't fucking infinite.
>>8091297
wrong
>>8092112
Yes, I agree. But I dont think that they give proof about "the Four Color Theorem can be solved with this amount of step". Same with Kepler Conecture. Or am I wrong?
>>8092146
Bitch, I'm fucking wrekt you. Sit your ass down or I big slap you with my nigga cock. I did say WHAT IF. Learn to read nigga
>>8091297
You can sum it but it does not converge. You can say the sum of the natural numbers is -1/12 though. Definitely not converge though.
>>8091297
Ok you wannabe-Grothendieck, consider the following:
1+1/2+1/3+1/4+... >
1+1/2+1/4+1/4+1/6+1/6+1/6+... =
1+1/2+(1/4+1/4)+(1/6+1/6+1/6)+... =
1+1/2+1/2+1/2+... = infinity
So,
1+1/2+1/3+1/4+... > Infinity
So the sequence diverge
>>8093505
You mean the
1+2+3+4+......= -1/12 ?
I gave up my common sense when I found out that it is used with remarkable accuracy in experiments regarding Quantum mechanics. (I think it regarding the kashmir effect or something)
>>8093805
You never even implied finite sum. And even of you did that'd be retarded since all finite sums are a finite number.
>>8093514
are you fucking retarded?
>>8094578
>And even of you did that'd be retarded since all finite sums are a finite number.
Exactly. So a finite summation of 1/n is finite and hence convergent.
>You never even implied finite sum.
Yes I did, otherwise 1/n wouldn't converge and my answer would make no sense.
>>8095015
But you never said it was finite or infinite. And finite sums don't really converge they sort of add up I guess.
>>8096062
Does it make sense for the well known harmonic series to converge?
Of course it doesn't - any cretin would have inferred that as finite.
But I forgot, this is /sci/.
>>8091261
riemann zeta
>>8095015
>So a finite summation of 1/n is finite and hence convergent.
This is a pretty pointless statement
>>8091278
It's the divergent harmonic series... that's 11th grade math.
A = 1 + 2 + 3 + 4 ...
A - A = 1 + (2-1) + (3-2) + (4-3) ...
0 = 1 + 1 + 1 + 1 ...
hurr durr rumanujan is geniouse
> inb4 incompleteness theorem
> kill yourself
>>8096358
Can I show what like what?
Both posts are mine fyi.
>>8096394
>incompleteness theorem
That has nothing to do with it.
Also, those equal signs aren't equal signs in the sense that you're used to.
>>8096394
>A = 1 + 2 + 3 + 4 ...
[math] A= \infty [/math]
>A - A = 1 + (2-1) + (3-2) + (4-3) ...
[math] A-A= \infty - \infty [/math]
>0 = 1 + 1 + 1 + 1 ...
>implying A-A=0
[math] \infty - \infty \neq 0 [/math]
I cant bother to all of you asshole, so I'm just going to give your asshole a good cleaning.
What i meant by >>8091278 is that the sum It is an INFINITE sum.
Consider again the fucking example:
1+1/2+1/3+1/4+1/5+1/6+1/7... >
1+1/2+1/4+1/4+1/6+1/6+1/6+... =
1+1/2+(1/4+1/4)+(1/6+1/6+1/6)+... =
1+1/2+1/2+1/2+... = infinity
So,
1+1/2+1/3+1/4+... > Infinity
So, the infinite sum of harmonic series diverge. This is a comparison example. Check Wikipedia for more.
>>8096629
It is counterintuitive. But, so what? Imaginary number is counterintuitive as well but you dont hear mathematician complain about them anymore
>>8096629
There was no need to specify that. When you said summation, it is implied to be an infinite sum because you didn't declare any bounds. The infinite sum from 1 to infinity is the most common/standard sum. I understand your frustration, just try to contain your rage. This is a "math that triggers you" thread so there are gonna be some trolls that are trying to trigger you.
>>8096636
Thanks anon, guess this is bound to happen since we cant even trust our own axioms according to Godël.
>>8096111
Are you retarded?
All I was saying is that you did not even remotely state that it was a finite sum, and since we were talking about infinite sums everyone assumed you were talking about the infinite sum.
This has nothing to do with math, just your poor communication skills.
>>8091278
Actually, it has been proven that if you removed any term that contained a particular string of numbers, the series would converge.
https://en.wikipedia.org/wiki/Kempner_series
>>8098135
*all terms
Sorry for my shitty grammar.
>>8091853
lemme guess, the person ranting about purity in math is not an actual mathematician.
>>8096629
>1 + 1/2 + 1/2 + ... < 1 + 1/2 + 1/3 + 1/4 + ...
I'm skeptical of your proof because this is not true.
>>8092004
Who cares along as it gets proved? It's not my computer time they are wasting
>>8091853
>Unsolved math problem need to be solved in a diligent way, not a brute force way...
>I have no idea what I'm talking about but my opinion matters.
>>8091781
Only non-math majors or first years care about that relation.
>>8096629
Half of the responses agreed, and half were from either trolls or people with little math knowledge. Why did you come back with this wall of text? It's not counterintuitive unless you make an assumption about convergence purely based on decreasing terms, which would be silly.
>>8091781
Also no one mentions 2 - 2 = 0 is the same thing???
>>8092048
Thats right you /sci/ fag. Prepare your asshole cause it gonna get stretch real wide by the fucking AI. It finally time to become an AI personal bitch
>>8091781
Recenty I was teaching some highschoolers abt euler's formula, so I wrote down 3^2 + 4^2 = 5^2, and literally no one recognized it as Euler's formula. No one had ever taught them that they're the same thing!
>>8094889
He's a weeaboo. What did you expect?
>>8091261
robinson's principle is kind of upsetting
