Question

How come x/0≠∞?

Answer 1

do you know the function y = 1/x?

Answer 2

because the limit does not exist.

f(x) = f(x) only if the limit exists at x

Answer 3

In my opinion this whole question is a bit unclear. To say that anything is equal to infinity is wrong because infinity is not a number. In limits things can 'tend to infinity', but 'equals infinity' is a bit like 'equals purple'.

Answer 4

On the other hand, the idea is that in some sense x/0 is (basically) like asking "0 times what equals x?" no matter how large of a number you multiply zero by it will never get any larger, so you can say that you would have to multiply it by infinity. I think this confuses the issue though as again, infinity is not a number, and you can't actually multiply by an infinite anything, you can only say that the limit tends towards +/-infinity, which is the same thing as undefined.