> It's theoretically impossible to compute with the general reals. Full stop. You could limit yourself to the computable numbers. Although you do have an issue

> It's theoretically impossible to compute with the general reals. Full stop. You could limit yourself to the computable numbers. Although you do have an issue determining equality on general computable numbers... But yeah, I would agree that floating-point is generally the best compromise out there for a general-purpose computational approximation to real numbers.