It's always going to be an approximation, and if you do some serious work with computer graphics you'll say some point maybe get a chance to see that the limits of floating point numbers aren't actually as large as they seem. Double precision is way bigger than single precision but still, if computers could actually "reach infinity" there wouldn't be any issues with floating point error in sensitive calculations. But the fact of the matter is that there is.

And at any rate, "infinity" is not a single value to be reached.

Take an analysis class and you'll understand this better!