Veeky Forums btfo

Veeky Forums btfo

Other urls found in this thread:

youtube.com/watch?v=w-I6XTVZXww
m.youtube.com/watch?v=sD0NjbwqlYw
wolframalpha.com/input/?i=sum n, n=1 to infinity
wolframalpha.com/input/?i=sum n*((-1)^(n-1)), n=1 to infinity
twitter.com/SFWRedditImages

>"Result" of the "infinite" "series"

>(((result))) of the (((infinite))) (((series)))

Can someone explain this fucking meme to me? How the fuck do you add a bunch of positive numbers but end up with a negative one?

>divergent result

youtube.com/watch?v=w-I6XTVZXww

>look mom I posted it again

also a bunch of integers and you end up with a fucking fraction

This should be proof that our universe is running on some kind of machine in which the numbers tick over from infinity to -1/12.

Possibly indicating that -1/12 is the 'first' number.

No.

hey guys... guys listen...

guys, wait, listen....

if you.... hey, listen...

if you add up all the positive numbers, they equal less than nothing.

Then why the hell does adding numbers eventually go to a lower number than where you start from discontinuously?

There's clearly one other system that behaves like this...

This is the quality of the content of the most popular mathematics youtube channel. Jesus christ

Someone help me understand why they take the average of natural numbers. If there's no meaningful value in the pattern between each N number, why would you take the average? That's where the fraction comes from, but it doesn't make any rigorous sense, and I say this as a mathematician.

It's called "analytic continuation". That's when a series doesn't converge, but analytic techniques are used to determine a specific numerical "result" for it anyway.

The classic example is the geometric series: the sum of x^n for all integers n > 0. If |x| < 1 then the series converges to 1/(1-x). If |x| >= 1 then the series diverges, but you can still often plug x into 1/(1-x) to get a result via analytic continuation.

Obviously, Σx^n is not the same function as 1/(1-x). Even though they yield exactly the same values for |x| < 1 -- that's not enough to conclude that they are the same function. You need agreement on the entire domain to claim that two functions are the same.

HOWEVER -- When one of the functions becomes undefined on some part of the domain, then you can use the other function to "extrapolate" (informally speaking) to get a "result" for the undefined function.

That's what people are doing when they claim that Σn has a "result" of -1/12. It doesn't really, but if you perform analytic continuation techniques on it (actually on a more general function called the "Riemann zeta function"), then you get -1/12 as a result of that analysis.

m.youtube.com/watch?v=sD0NjbwqlYw

Watch this entire video to understand what's going on.

Essentially, map the output of the riemann zeta function and notice its only defined for when the real part of s is greater than one.

The leap mathematicians do is say "well look at this graph, it makes an abrupt stop because we ran out of inputs. Let me reflect the graph vertically and now I have outputs for all complex numbers."

They literally just make up a mapping that LOOKS right because they just reflect the mapping function accross a vertical axis and say "there you go, everything is defined" and suddenly you get a lot of ridiculous formulas.

This is simply a useful mathematical tool, nothing more. Infinity doesn't equal -1/12 unless you suspend reality and make up shit.

you can't actually add anything up to infinity unless you suspend reality so shut up

You can if each term is shrinking at a continuous rate. You shut up.

See here... the thing about this meme is that everyone should have said, "Oh! There is some problem with out analytical framework," but instead they said, "Fuck it! Let's go with it and point all the attention to the result but never the analytical framework!!!"

>the thing about this meme is that everyone should have said, "Oh! There is some problem with out analytical framework,"

I'm so tired of people with no grasp of what's going on saying shit like this. Everyone knows the series diverges and that the -1/12 value is an analytic continuation of a function that matches the series where its image is defined, not a "value of the series." It's just a fucking internet meme.

Is this result actually useful in any purpose?

its not 1+2+3+4...

its 1-2+3-4...

> its 1-2+3-4...

That series yields 1/4 as a result of analytic continuation.

OP's pic is showing the correct analytic continuation for 1+2+3+4...

Umm excuse me

Ive taken algebra 2 and im pretty sure i know what im talking about

For 1+2+3+4+... see:

wolframalpha.com/input/?i=sum n, n=1 to infinity

For 1-2+3-4+... see:

wolframalpha.com/input/?i=sum n*((-1)^(n-1)), n=1 to infinity

> Ive taken algebra 2

Good for you. But when you disagree with Wolfram Alpha, then you've got some serious explaining to do.

>clearly falling for a troll

The reason why people pretend like it's actually valid especially in phyiscs is because Gauss used divergent serieses to predict the position of a comet that was lost using a divergent series

-1/12 is a place holder for infinity
Just like 0 is a place holder, not a number.

Also, prime numbers don't want to be divided into equal integers. The number 1 is a nigger for this reason.

>pretend like it's actually valid
Define "valid".
Within the theory of analysis, it's a wrong claim. You can prove its negation.
But that's also already it. It's wrong in some much use framework, and not more. It's not "untrue" in any platonic sense.

this is the only correct answer

same way you can add rational numbers and end up with irrational one