Yes. A computer scientist should know how numbers are represented and not expect non-representable numbers in that format to be representable.

0.1 is just as non-representable in floating point as is pi as is 100^100 in a 32 bit integer.

Terminating dyadic rationals (up to limits based on float size) are the representable values.

I’m not sure if you got my joke but I referred to the mathematical philosophy, finitism.

That's essentially what you already do for integer arithmetic.

0.1 is of course a real number, but let A \in R the set of actual numbers... (/s)

The funny thing is, according to infinitists real numbers are not real. But I do like the concept of the set of actual numbers.

I don't know whether I'm an infinitist, but I personally think "real numbers" is the most ingenious marketing term created by mathematicians...

\infty is an actual number not in R

Should be \subset.