"nice, correct numbers" end somewhere between 1/3 and sqrt(2)

so in reality, it's just "pick your own poison" to various degrees...

tialaramex 5 days ago | parent | next [-]

The square root of two is still a computable Real. We choose not to cope with that, but it's not actually impossible it was merely inconvenient. I've mentioned elsewhere that my Rust care realistic is quite happy to work with these numbers e.g. take the square root of ten, and the square root of forty, multiply them together and get the quite ordinary integer twenty.

The non computable reals are a huge problem because, as their name suggests, we can't compute them - and in the strict sense that's Almost All reals, but none of the ones you're thinking of are non-computable so you'll likely be fine.

For the merely rational numbers like a third, or sixteen hundred and five sevenths, it's even more so a matter of choosing not to address it rather than it being out of reach.

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GolDDranks 5 days ago | parent [-]

The problem with computables is that equivalence between them is only semi-decidable. (If the two numbers are different, it is decidable, but if they are not, it isn't. The problem is that you don't know if they are different a priori, so you might get lucky and find difference, but you might as well not.)

We know for sure that algebraic numbers behave nicely in terms of equivalence, and there are other, bigger number systems that are conjectured to behave nicely ( https://en.wikipedia.org/wiki/Period_(algebraic_geometry) ), but the problem with these and computers is that they are hard to represent.

	▲	tialaramex 4 days ago \| parent [-]
		Yeah, all these types have problems, we've decided to put up with the IEEE floating point numbers, we could have chosen to have the big rationals, or drawn any other line. I don't disagree that there's no satisfying "correct" answer but it's a little disappointing that programmers so easily accept the status quo as though nothing else could be in its place. Maybe Python having automatic big numbers like Lisps often did will help introduce new programmers to the idea that the 32-bit two's complement integer provided on all modern computers isn't somehow "really" how numbers work.

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int_19h 5 days ago | parent | prev [-]

Even so, we don't need to pick the more potent poison. And most certainly not when we had decades of awareness about better alternatives.

There's really no excuse for a modern PL to not have, at the very least, overflow detection by default.