Infinitely many infinitely small numbers.

[zetafunction]

HARMONIC series is divergent, but REGULARIZABLE

\sum_{n=1}^{\infty} \frac{1}{n} = - \frac{\Gamma '(1)}{\Gamma(1)}

the idea is that Harmonic series is the logarithmic derivative (a=1) of the infinite product

\prod (n+a) which can be 'regularized' to give e^{ - \zeta ' _{H} (0,a)

here the Zeta function is the Hurwitz one , the above is the definition of zeta-regularized determinat

 

[HallsofIvy]

No typo.

These questions stem from a thread that was around a several weeks ago, where it was stated that \frac{1}{\infty}=0. My real question that I’ve been building up to is: how can \lim_{n \rightarrow \infty}\sum^{n}_{i=1} 0 = 1

Then don't worry about it
\frac{1}{\infty}= 0
is not true in standard analysis.

 

[arildno]

Then don't worry about it
\frac{1}{\infty}= 0
is not true in standard analysis.

This thread is 6 years old, Halls!