>Real numbers can’t be perfectly represented in hardware simply because there are infinitely many of them.
There are also infinitely many integers, but we can represent them just fine inside a finite bound. The problem with reals (and rationals to a lesser extent) is that, within any range we are interested in, a single real number can be infinitely 'long'.
There are also infinitely many integers, but we can represent them just fine inside a finite bound. The problem with reals (and rationals to a lesser extent) is that, within any range we are interested in, a single real number can be infinitely 'long'.