Consider the wheel made by extending the real numbers into a wheel. Are $1/0$ and $2/0$ distinct? Or are they the same? I can't seem to derive either result from the rules. Only that $/0 + /0 = 0/0$.

Is it that $/0 +$ finite $= /0$? How do you prove that?

Or are these things not provable, but rather just one possible wheel that you can make out of the real numbers?