What happens when we divide zero by zero?

Question

I know that 0/any number=0 and any number/0=no answer, (negative) infinity, undefined. So, what happens if we divide zero by itself? Is it zero? Is it infinity? Well, infinity isn't a real number, but let's cut to the real chase. Let's say there are two points on a coordinate plane put together. How will we know what line to draw? What slope does it have? We know that the x- and y-intercepts are the same. What happens when we divide zero by zero?

Answer 1

0/0 is undefined, but if you want a value, this is best done using limits. 0/0 can be approached in multiple ways.

First of all, there is the function x/x. The limit of this function as x goes to 0 is 1.

There is also 0/x, the limit of this function as x goes to 0 is 0.

And the last one I will discuss: x/0 as x goes to 0. This limit does not exist.

Of course, you can think of many more limits.