How much is 0 : 0 ?

Answer

This question has already been discussed on this forum:
http://www.ikhebeenvraag.be/scholars/vragen3.jsp?id=7835

The bottom line is that 0:0 is a so-called indeterminacy. So you can’t put a number on it.
0:0 can only arise when you take the fraction A/B of two quantities A and B that both go to zero in limit at the same time. As long as they are not equal to zero you can calculate their fraction, and then you have to look at what number that fraction goes, while A and B go to zero.
The result can be anything : 0, 1, 7, -5, plus infinity, minus infinity…

That’s why 0:0 is called an indefinite, you can’t calculate it, you can only approximate it, but even then the result depends on the situation, and that result can be anything.

In short: 0:0 does not exist.