What is 0 / 0?

Is the valué that you want $\frac{\sum_{x=1}^{\infty}\frac{1}{x^{2}}}{\sum_{x=1}^{\infty}\frac{1}{x^{2}}}$

Do not think of zero as a number but as the limit of a series

$\frac{\sum_{x=1}^{\infty}\frac{1}{x}}{\sum_{x=1}^{\infty}\frac{1}{x^{2}}} =\rightarrow \infty$ Being the largest numerator $\frac{\sum_{x=1}^{\infty}\frac{1}{x^{2}}}{\sum_{x=1}^{\infty}\frac{1}{x}} = \rightarrow 0$ And in this case the denominator is bigger it goes to zero

$\frac{\sum_{x=1}^{\infty}\frac{C}{x^{2}}}{\sum_{x=1}^{\infty}\frac{1}{x^{2}}} = \rightarrow C$ It is UNDEFINED

$\large0/0$ not possible. Hence there is no answer to this.

Here is my theory. I'm basing this off of binary a bit. If you were to make a binary divider in anything that has a sort of circuitry and can make logic gates (I used Minecraft), then you would know how it works. It check from left to right to see if the dividend can be subtracted by the divisor. If it can, then that would be marked as a 1. If not, then it would be marked as a 0. It keeps on doing this until either it stops or it keeps on going after the decimal and won't stop. If you leave all inputs off, it will show all outputs as 1. That is because you can subtract 0 by 0, so it'll mark the first number as 1. Then it will check the other number, which will still give the same result. So if you divide 0 by 0, you're constantly dividing, meaning that the number of times you divide it is infinite, so the answer, in my opinion, is infinity. I will make a youtube video describing this a bit better. The rest of my channel is a bit cringy, but you don't have to watch those. Just look out for that video.

Another thing to prove that 0/0 is infinity is if you multiply anything by 0, you would get 0. 1 x 0 = 0, 2 x 0 = 0, or n x 0 = 0. Everyone knows that if you flip the equation, including the answer, then you get the equation for the opposite operation, like if 2 x 2 = 4, then you'd swap the equation to get this: 4 = 2 x 2. You would then turn this into the opposite operation equation. So it'll be turned into 4 / 2 = 2, which is true. If we were to do that with n x 0 = 0, then it would be 0 / 0 = n, and n could literally be anything.

There is no answer for 0/0.