Math is BROKEN: 1x2x3x...= √2π

#shorts

In this video we show how mathematics can give unbelievable results! We will utilise the Riemann-Zeta function to show how the product of all infinite natural numbers equals square root 2 pi.

[Adomas_B]

This is just 1+2+3... = -1/12 all over again

[ChechoColombia]

For s<1 the anwers are gonna be nonsense.

[rektlzz]

Pretty sure that the derivative of the Riemann Zeta function isn't defined at 0 over the reals. Although I would assume that you took the value of the analytically continued Zeta function which gives nonsensical answers, but still pretty cool nonetheless.

[alonvinkler]

nice trick, too bad some of us are aware of what the zeta function is and are aware that it won't work in this case.

[nomzz]

The Riemann Zeta function is only defined as the infinite sum of 1/n^s for s>1, for s=0 the zeta function does not represent the value of the infinite sum of 1/n^s, it represents the analytic continuation of it.

[eduardoGentile]

The answer Is Always riemann zeta bullshit when you see those kind of things

[mayankshekhar]

That's why we use rigorous definitions when doing things we have little intuition behind it prevents this non sensical answers from popping

[rajakannant]

Product of squares of all natural numbers
1²×2²×3²×4²×5²×....=2π

[Rando]

The series definition of the Zeta function only applies for Re(z)>1. The rest of it is defined via analytic continuation. Using the series definition for numbers like 0 or -1 is just wrong.

[marcellomarianetti]

that's interesting! but doing exp(ln(...)) means assuming the infinite Product converges, it's the same trick for 1+2+... = - 1/12, the Ramanujan sum

[abdulkhadarainur]

Actually, I don't think derivative of Riemann Zeta is defined at 0. You used Analytical continuation but that, is no less than a guess. You should provide the context before making such videos.

[hmm]

No bro, you are kinda wrong the derivative of riemann zeta will not be go to that

[Ebaadsiddique]

Yeah that simply can't be the case. I don't need a degree is mathematics to know that.

[DrAYOUBZ]

There is equation between -1/12 and sqrt(2pi) that by use natural log

[VincentKok]

You can't mess with this infinite product using ln because it diverges to infinity.

[velkykoblyh]

I mean the product rule for the logarithms only works for finite products, so this argument is a little shady🤭

[AngelGamer-qgcq]

Occam's Razor: the simplest solution is usually right; sqrt(2pi)~2.5; 1*2*3 = 6, and this equation only grows as it's multiplying to infinity

[Yu-Gi-Oh]

Idc what those silly magic men say,
1x2x3x4... is infinity idc what math bs they do

[subarnasubedi]

Here is a simple example why this happens 1+x+x^2+x^3+....=1/(1-x) for -1<x<1 . If you plug in value outside 1 to compute 1/(1-x) you will get weird results, this is called continuation of function beyond its natural domain.

[Redman]

Uhhh ok im not a mathematician but i knew this was bullshit immediately lol.