/sci/ - Science & Math

[Anonymous No.10538162]

reminder that if you believe that the summation of all natural numbers equals - 1/12 you're fucking retarded

[Anonymous No.10538164]

>>10538162
>natural numbers
it's complex numbers, so no problemo
https://youtu.be/sD0NjbwqlYw?t=10m

[Anonymous No.10541195]

>>10538162
it is though

[Anonymous No.10541203]

math is retarded

[Anonymous No.10541274]

>>10538162
Reminder that if the sum of all natural numbers being -1/12 isn't instantly intuitive to you you're basically braindead

[Anonymous No.10541374]

>>10538162
It literally doesn't because the proof of this requires breaking with the widely accepted definitions of addition.

[Anonymous No.10541417]

>>10538162
>it's a "some perma phd failure picks some cherrypicked
border definition and implements it in some basic equation to fuck it up and be le ebin joker"

And they wonder why people hate mathematicians

[Anonymous No.10543087]

>>10541374
This.

[Anonymous No.10543219]

>>10538162
define summation

[Anonymous No.10543640]

The problem is that zeta(-1) is -1/12, but people assume the zeta function is equvilent to the infinite sum on all numbers.

[Anonymous No.10543647]

>>10541374
Say a little more?

[Anonymous No.10543653]

>>10543640
Prove it's not retard, I watched a video from numberphile on this subject so I know a thing or two about this.

[Anonymous No.10543676]

>>10543653
Give this man a PhD.

[Anonymous No.10543677]

>>10541374
>the widely accepted definitions of addition.
no one cares about your "widely accepted" definition, you use a bad definition

>>10538162
give a reason against it then
and not "the partial sums diverge"
the partial sums are just from your arbitrary definition

[Anonymous No.10543687]

>1+2+3+4+5... = -1/12
>-1/12 = 0.833333333
>therefore 1+2+3+4+5... = -0.83333333
>sum of all natural positive number (up to infinity) is a FINITE negative number

To add salt to injury, the absolutely retarded explanation to this is
>xD uhh let's manipulate some other infinite additions
>1-1+1-1+1-1...
>would be undefined right? NOPE XD
>since ummm if you stop at one point you would get zero and on the next one you would get 1 LETS ROUND IT UP!
>1-1+1-1+1-1 = 0.5

Such a load of bullshit.

[Anonymous No.10543697]

>>10543687
>since ummm if you stop at one point you would get zero and on the next one you would get 1 LETS ROUND IT UP!
thats not the explanation at all

[Anonymous No.10543702]

>>10543697
Let's hear it then.

[Anonymous No.10543711]

oh cool it's this thread again
now i get to read the wikipedia article on ramanjuan summation again

[Anonymous No.10543714]

>>10543653
Based and number p(h)illed

[Anonymous No.10543780]

>>10543702
The series of the n first terms of any series is
a
a + b
a + b + c
a + b + c + d
...

right? this is just the partial sums
now doesnt it make perfect sense for
a + 1/2 b
a + b + 1/2 c
a + b + c + 1/2 d
a + b + c + d + 1/2 e
...
to equal the exact same thing?

we're accelerating the convergence
and with the second collection, the partial sums are always exactly 1/2 with 1-1+1-...
so the limit trivially exists at 1/2

and also
[math]\displaystyle
\space \space \space G = 1 - 1 + 1 - 1 +1 -1+... \\
-G = \space \space - 1 + 1 - 1 + 1 - 1+... \\
-G = \space \space -1 + G \\
\space \space \space \displaystyle G = \frac{1}{2}
[/math]

[Anonymous No.10543810]

>>10543780
You're talking about partial sums on an infinite series.

Down to the most barebone explanation possible, the sum of all natural numbers is either undefined or infinite, because there's no way to calculate a finite answer out of an infinite calculation.

As for 1-1+1-1 etc. it's the same thing, you can arbitrarily "end" your calculation and get 0 or 1, but if you really mean it when you say "the sum never ends" then you can't give it a finite answer.

[Anonymous No.10543825]

>>10538162
I stopped math in grade 11 and never took anything in university and even I know that a divergent series sums to infinity

[Anonymous No.10543826]

>>10543810
>but if you really mean it when you say "the sum never ends" then you can't give it a finite answer.
totally unsubstantiated

[Anonymous No.10543827]

>>10543780
You can't alter the order of addition with complex numbers

[Anonymous No.10543833]

>>10543827
where did the order of addition change

[Anonymous No.10543838]

>>10543780
Thats because G will equal 0 or 1 in the end, so you're simply manipulating it towards your point without account for both parts. Youre effectively averaging it

[Anonymous No.10543842]

>>10543833
In not adding the first 1 of G with the first -1 of G. You have to keep it in order

[Anonymous No.10543852]

>>10543838
>in the end
no

>without account for both parts.
the series approach the same value thing, how am i not accounting for everything?

>Youre effectively averaging it
im accelerating the convergence
it just so happens that accelerating convergence with an alternating series looks like weighted averages
https://en.wikipedia.org/wiki/Series_acceleration

>>10543842
they werent added together

[Anonymous No.10543922]

>>10538162
NHAE praise ababou

[Anonymous No.10543938]

Math isn't real retards.

[Anonymous No.10543970]

>>10543826
You can't define something that is infinite with a finite value, Wojack. Meditate on it.

[Anonymous No.10544041]

>>10543970
neat meta physics, but do you have any math at all?

[Anonymous No.10544146]

>>10543653
made me lol irl senpai

[Anonymous No.10544160]

>>10544041
I don't, because there'a no math needed.
Your averaging bullshit is the real metaphysics here.

[Anonymous No.10544188]

>>10544160
cope for retards, huh?

[Anonymous No.10544241]

>>10544188

[Anonymous No.10544347]

>>10544241
you have yet to write any actual math

[Anonymous No.10544677]

>>10543970
0.999...= 1
it sure the hell isn't >1

[Anonymous No.10544748]

>>10538162
it doesn't
1+2+3+4+... = -1/12 now add 5
1+2+3+4+...+5= 59/12 and continue doing so by adding 6, 7 and all other natural numbers

[Anonymous No.10545705]

>>10544748
>if i dont write the terms, they arent actually there
1+2+3+4+5+... +5 isnt equal to
1+2+3+4+5+...

[Anonymous No.10546702]

>>10544677
B8

[Anonymous No.10546774]

>>10546702
>[math] 0.999... \ngtr 1 [/math] is bait
k

[Anonymous No.10549060]

>>10544677
It doesn't equal 1, infinitely close to something doesn't mean you're there. It means the opposite: that you're NOT there.

[Anonymous No.10549181]

>>10549060
when 2 numbers are equal, if you subtract them you get 0
so whats 1 - .99...
keep in mind that "infinitely close to 0" doesnt exist, then 1/.00000... would be infinity, and we know infinity isnt a number

[Anonymous No.10549209]

>>10549181
define "equals"

[Anonymous No.10549227]

>>10549181
>we know infinity isnt a number
"We" need category theory and clearer terms.

[Anonymous No.10549232]

>>10543780
Intelligent shitposting. I wonder if there is some general rule along these lines that can be applied to the partial sums to give values to diverging series more-or-less consistent way?

[Anonymous No.10549253]

>>10549181
Serious question: does infinity have a reciprocal?

[Anonymous No.10549287]

>>10549253
Null o

[Anonymous No.10549291]

>>10549060
1/3 = 0.33333333...
1/3 + 1/3 + 1/3 = 3( 1/3 ) = 1
1/3 + 1/3 + 1/3 = 3( 1/3 ) = 0.99999999...
So,
0.999999... = 1

Funfact,
0.99999... x 2 = 1.99999...
0.99999... x 3 = 2.99999...
0.99999... x 55 = 54.99999...
So this doesn't even effect calculations. You just end up with a tail of 9s instead of the next whole number.

[Anonymous No.10549503]

>>10549232
The technique I outlined there is called Cesaro summation, more specifically it's the First Cesaro sum
https://en.wikipedia.org/wiki/Ces%C3%A0ro_summation

there are many more, Abel summation, Euler summation, Ramanujan summation is most well known, they generally fall under the name Abelian or Tauberian Theories
Hardy's book, Divergent Series is great
But yeah, the "consistent" ways are those done by good enough methods
https://en.wikipedia.org/wiki/Divergent_series#Properties_of_summation_methods
ie the Regular methods and the linear methods

>>10549253
no, only (non zero) numbers have reciprocals and inf isnt a number
though you can say the limit of 1/x as x approaches inf is 0

[Anonymous No.10549549]

>>10543780
>now doesnt it make perfect sense for
It really doesn't.

[Anonymous No.10549561]

>>10541374
Yeah, the Numberphile video on it was really bad. I think that's where all the controversy comes from. That = sign is what really triggers me.

[Anonymous No.10549564]

>>10549060
>infinitely close to something doesn't mean you're there
topkek, that's exactly what it means.
it's the finite ones that "don't get there"

[Anonymous No.10549723]

>>10549549
then i have some bad news for you

[Anonymous No.10550493]

If the sum of all natural numbers is -1/12 what is the sum of all integers?

[Anonymous No.10550555]

>>10550493
probably 0

[Anonymous No.10550902]

>>10550493
inf-inf, which is undefined

[Anonymous No.10550961]

>>10538162
>summation
>equals
Define these meme words

[Anonymous No.10551112]

∞<1

[Anonymous No.10551162]

>>10541274
if by intuitive you mean that even a retard would unconsciously infer the induction that if the sum is of all numbers positive, then whatever the answer is, its value must be at least as high as any one of the of the numbers summed, e.g. at least 1. If your answer doesn't fit this inference, then you should consider the possibility your answer is wrong, find a different answer, then and only then consider which one is more likely true, struggle with the apparent notion that all knowledge is necessarily just a scale of likelihoods, suffer an existential crisis, and kill yourself.

[Anonymous No.10551188]

>>10551162
induction only works for natural numbers, infinity is a natural you fucking idiot
>even a retard would unconsciously infer the induction that if the sum is of all numbers positive, then whatever the answer is, its value must be at least as high as any one of the of the numbers summed
and even a retard would say that if you only add rational numbers together you can only get a rational number, but thats not fucking true, maybe actually learn some math before you talk out of your ass on it
fuck yourself, you 3 iq condescending shit

[Anonymous No.10551247]

>>10549253
yes, [eqn]\infty * 0 = 1[\eqn]

[Anonymous No.10551491]

*Sums your divergent series*

[Anonymous No.10551999]

>>10551247
inf * 0 is undefined

[Anonymous No.10552154]

>>10543780
its not a series! what are you doing its the cesaro summations and its a limit and if you assume the sequence its convergent then you can define the value of the sequence G with the cesaro summation, but you assumed conditionally that diverges

[Anonymous No.10552162]

>>10552154
heh i meant *converges

[Anonymous No.10552175]

>>10543687
do not mess with rigorous math please, you are making a lot of assumptions and you cant just judge them with logic

[Anonymous No.10552187]

>>10552175
gr8 b8 m8

[Anonymous No.10552312]

>>10543687
I imagine there is a man who is constantly +1-1+1-1...+1-1 in his life.
What is this man? Is he 0? No. Because he exists. He is half a man. 1/2.
+1+2+3..+4+5. This is every natural number. So everything that exists in our universe. What is the sum? A negative. Why? Because it is not ours, but God has given it to us. And we owe to him. Moreover the fact that it is a mere -1/12 means that it is but a infenticimal fraction of his actual power.
Makes perfect sense to me.

[Anonymous No.10552466]

it's -1/8

https://www.youtube.com/watch?v=6FTwMUL69u0

[Anonymous No.10552469]

>>10551188
Sorry, m8, but all I read was "induction only works with" and "you fucking idiot." You seem to be purposely misunderstanding what I mean by "induction," and purposely disobeying the principle of charity. Induction, in logic, merely means to infer from the general to the specific, which applies to inference from all types of numbers. I'm not even sure how you've implicitly defined it, but I assure you that your misunderstanding does not imply I am the one who's wrong, you goddamn fucking retard. People as stupid as you should and will be killed.

[Anonymous No.10552472]

>>10538162
Are you still memeing about this?
You're like a year late.

[Anonymous No.10552494]

>>10552469
your "proof" of "if you add n positive numbers, you get a positive" is where you use mathematical induction you uneducated twat
>if the sum is of all numbers positive, then whatever the answer is, its value must be at least as high as any one of the of the numbers summed, e.g. at least 1.
>If your answer doesn't fit this inference, then you should consider the possibility your answer is wrong
your "intuitive" proof of this is done through induction, which is not valid for an infinite sum

>but I assure you that your misunderstanding does not imply I am the one who's wrong, you goddamn fucking retard.
you are the one with the misunderstanding, "if you add infinite positive numbers, you get a positive" is not true, you have assumed it is

>People as stupid as you should and will be killed.
you are posting on a topic you know nothing about, there is nothing stupider than that

[Anonymous No.10552566]

>>10538162
>>10541274
Reminder that if you don't understand that the equal sign there doesn't have its traditional meaning, you're fucking retarded.

[Anonymous No.10552577]

The most irritating thing about these troll posts like -1/12 and .999... isn't even the obviously pretending OP. It's retards like these
>>10543780
>>10543677
who have no understanding of what they're talking about but they memorized some facts so they're obviously much smarter than the people who haven't. You have equal understanding of it as the OP pretends to have, which is 0.

[Anonymous No.10552645]

>>10552577
kys

[Anonymous No.10552655]

>>10552312
Fuck you stop breaking my brain