ITT: counter-intuitive mathematical facts https://www.youtu

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>Gamma exists
>Counter-intuitive
Apex kek.

wtf does -1/12 mean? Call me a brainlet but it doesn't make any sense

>>8539392
It doesn't, the sum of all positive numbers is infinite because infinity is infinite. But what can you expect from a poo in loo with no education trying into mathematics?

>>8539396
Actually I just read a few things about it, it seems Analytical Continuation is used to obtain an equation of the same value which is actually possible to calculate, the equal in 1+2+3+4+5...=-1/12 actually measn that such series is associated with said fraction, not that it's the actual result of adding all of those numbers.

Also it has come up in physics which I guess is an indicative of it being at least partially right

>>8539453

It is indeed analytic continuation.

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

Not very rigorous, but it's better than most of the videos I've seen on the topic because it actually talks about the theory behind it a little, rather than just saying dude [math]\sum_{n=1}^{\infty}n = -1/12[/math] lmao

>>8539341
What I want to know is whats the 'sum' of the harmonic series? 'sum' as in -1/12 sum, not infinity sum.

>>8541338
I should have googled before posting this, it turns out
[eqn] \sum_{n=1}^\infty \frac{1}{n} = \lim_{h\to0}\frac{\zeta(1+h)+\zeta(1-h)}2=\gamma[/eqn]
with gamma the Euler–Mascheroni constant. pretty cool

I think it's still kinda weird how you can use the pigeonhole principle to prove that there are people in London with the exact same number of hairs on their head.

>>8541494
how is that weird?

you can also use it to prove that somewhere in the world, there are 2 people with the same number of fingers.

>>8541501
The finger thing is intuitive, the hair thing isn't

>>8541345
Wait. 1 + 1/2 + 1/3 + ... is a divergent Riemann series.

>>8539396
Well while it's certainly not true, it has a basis (mainly Analytical continuation). Don't try to be a smartass.

>>8541509
yes, its z(1) = infinity, but you can use its Cauchy principal value which is gamma