Number theory discussion regarding floats, ints and NaN/Inf

I think that many of these suggestions regarding float (another that I saw is this one) come inspired from looking at floating point numbers with bounded precision as real numbers with a deficiency. Floating point numbers with bounded precision are a structure of its own and the boundedness of the precision is a feature. As such, I see having functions like +, -, *, /, and Euclidean division //, % as internal operations as useful. And as a consistent feature. You do operations on its values and obtain some other of its values. Compare to int, which does model \mathbb{Z}, assuming sufficient memory, in which the same is true.