For example, pi can be computed to arbitrarily many digits, but could only even in principle be accurately represented with physical objects to a precision that many humans could memorize easily. This is thanks to physical constraints such as "diameter of the observable universe" and "Planck length", at a minimum.
Even if pi is an approximation, it is still representable mathematically. Floating-point arithmetic is an algebra (in this case, a magma [1]), which can be studied mathematically.
