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!