We can't count to i or pi any more than we can count to infinity, yet we claim the first two are numbers and the third can't possibly be.

In the function f(x) = 1/x, infinity seems to be reached at x=0. If you complain that you can't tell if it's + or - infinity there, well, could you be making an unfounded assumption that those are not the same? On the graph, they appear to be the same. If we posit that 1/x is in some sense continuous at x=0, then + and - infinity are the same number, and it is reached at x=0.

We can't count to it, but we can reach it with familiar operations.