Analysis

analysis, as you said. try Tao's Analysis I for a great introduction

Thanks for a legit answer!

Anything Fourier series.
Basically it is an infinite dimensional vector space where the basis vectors are the functions sin's and cos's of all integer frequencies.

en.wikipedia.org/wiki/Parseval's_theorem

Dirichlet kernel and Fejer kernel for convergence criteria

Hell give Euler-Maclaurin formula a try

The subtleties of complex exponents and branch cuts...

Yes

You are ok with 0.33333...=1/3
Are you ok with ...99999.0=-1?

en.wikipedia.org/wiki/Two's_complement

For inspiration

>infinite dimensional vector space
>basis
No such thing.

en.wikipedia.org/wiki/Hilbert_space

SMD

So? That still isn't proof that infinity = -1/12

>SMD
Shaking my dick?