Daily reminder that 1 - 1 + 1 - 1 +... equals 0.5.

>>8593130
[math] \mod \mathcal{R} [/math]

>>8593130
I like to think of it as the tops and bottoms of a sine wave and then its position would "average" at exactly between 1 and 0 = 0,5

>>8593229
It's still bullshit without any understanding of divergent series.

Fejér's theorem

Anyone know where one could find a rigorous treatment of this series? I've seen the numberphile vid on it but that wasn't really satisfying and I haven't taken analysis yet.

>>8593246
Triple integrate it and it instantly becomes more rigorous

>>8593246
the rigourous treatment is that it diverges. Thats all there is too it, it doesn't equal anything. You can't do anything to it, you're welcome.

>>8593246

if you use it to prove that 1=2 nobody will give a fuck but maybe if you generate a pretty fractal then suddenly rigorousness doesn't matter

>>8593246
https://www.youtube.com/watch?v=sD0NjbwqlYw

This should start you off; not 100% rigorous but it's a much better explanation than numberphile's. Look into the riemann zeta function and analytic continuation. The meme has SOME grounding, problem is numberphile assumes you're an idiot and tries to explain it by rearranging a divergent series rather than using complex numbers.