I have this idea on how to sum supernatural numbers assigning them a finite value in a way similar to how we assume that the sum of every natural numbers from 1 to infinity equals $-\frac 1 {12}$. Let's take for example the number: $\omega_2=\prod_{n=1}^\infty2$
Which can be written as: $\omega_2=2\times2\times2\times\dots$
And with basics power properties we can rewrite it as: $\omega_2=2^{1+1+1+\dots}$
Now recalling Riemann's Zeta function and it's analytic continuation we have:
$\omega_2=2^{\zeta(0)}=2^{-\frac 1 2}={\sqrt2\over2}$
We can extend this to every number of the form: $\omega_s=\prod_{n=1}^\infty s={\sqrt s\over s}$ where $s$ is prime.
We can easily now sum supernatural numbers, for example:
$\omega_2+\omega_3=2\times2\times2\times\dots+3\times3\times3\times\dots={3\sqrt2+2\sqrt3\over 6}$
Did I made something wrong ? Is this useful in some ways ?