> the increasing use of real variables in software This betrays the complete lack of mathematical qualification evident in the rest of your comment. IEEE numbe

> the increasing use of real variables in software This betrays the complete lack of mathematical qualification evident in the rest of your comment. IEEE numbers don't even pretend to be the reals. The most that can be said for them is that they're two copies (positive and negative) of a very small subset of the nonnegative rationals, adjoined to a couple extra symbols (+inf, -inf, NaN), with really wonky operations to work around the obvious non-closure of the rational subsets under standard mathematical operations (let alone the approximations to transcendental functions). I think it's important to be extremely clear: this is not at all like the mathematical reals, not even a tiny little bit. The use of IEEE numbers in serious applications (Bitcoin, iiuc) is truly frightening. They should be considered "useful for computer graphics" (although I can't say whether modern gpus are using IEEE numbers; they're at least useful for software rendering) and nothing more.