OK can somebody explain this bullshit to me I watched the numberphille

>>8541391
underage b&

Is it truth this has applications in physics or just idiots creating sources out of nowhere?

>>8541403
In the video he refers to the formula being used in a string theory textbook.

Since strong theory has yet to be proved or unproved (in fact we don't know if we can ever prove it) then pretty much amounts to nothing real.

>>8541409
It's also used in quantum field theory model. I mean the sum "1+2+3+4+..." has a Wikipedia article with that name, why not start there.
https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF#Physics

>>8541391
>I watched the numberphille video and he basically seems to pull it out his ass uising high school math
Yes, he did.

There are formal, rigorous demonstrations of the phenomenon. That video is not one of them.

>>8541391
This is what I call, universe overflow

>>8541391

It is bullshit, from the wikipedia article mentioned by anon:

> Generally speaking, it is incorrect to manipulate infinite series as if they were finite sums. For example, if zeroes are inserted into arbitrary positions of a divergent series, it is possible to arrive at results that are not self-consistent, let alone consistent with other methods

With some imagination you could make that infinite sum be another number, perhaps whatever number you want

It would be like if I tell you 1 + 1 = 3, and the demostration is that:
1 + 1 = 2
adding 1 to the right side
1 + 1 = 2 + 1
then
1 + 1 = 3

the math is wrong, adding one to the right doesn't keep the equality on both sides.

>>8541391
>S1 = 1 − 1 + 1 − 1 + 1 − 1 + 1 − 1 + … = 1/2

This is where they are wrong. This sum actually diverges, however, we have [math]S_{2n} = 0[/math] and [math]S_{2n+1} = 1[/math].

One approach to this divergent series is to say the "mean" of the possible values is the convergence. In this case, S = 1/2.
This is not the usual definition of the limit of the sum, however.

>>8541391
the sum under natural numbers is closed, so the result must be a natural, not a rational number

>>8541391
it's only classified as such when defined under the Riemann-Zeta function defined outside of the original set domain of the function (-1)

watch this video to get a better understanding

https://www.youtube.com/watch?v=sD0NjbwqlYw

>>8541721
Thanks ! Nice voice, nice visuals, calm and rational.

Yet that's not false an equation of the quantum theory use this (theorem of Goddard-Thorn)

>>8541721
That was really good, thanks.

>>8541721
ty

>>8541391
Check out 3blue1brown on youtube. He has two videos explaing this, one called "What's it like to invent math" and another about the riemann zeta function.

>>8541391
Series doesn't converge absolutely => weird shit happens if you try to do things with it like permuting members, simply adding brackets or, in this case, try to analytically extend the function so that it "seems" equivalent to the series.

>>8541391
The zeta function of -1 is -1/12 thats it and the only reason its important