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>You can't put a rational multiple of pi exactly into a computer. Of course we can: "1/2*pi" >You can't get a rational multiple of pi exactly out of a compute
by mike00632 8y ago
>You can't put a rational multiple of pi exactly into a computer.
Of course we can: "1/2*pi"
>You can't get a rational multiple of pi exactly out of a computer.
Using the same limitations you seem to have in mind, we can't get one third exactly either.
>...countable sets are still infinite but they're better-behaved than bigger sets.
Yes, and that is surprising because we do have numerous clever applications that skirt around most of the intractability of exotic real numbers. That is why I think this paper is a bid deal, especially because it points to the cardinality of the real numbers instead of, say, their inclusion of the uncomputable numbers.
- lmm 8y ago> Using the same limitations you seem to have in mind, we can't get one third exactly either. We can work with exact rationals; we can do arithmetic on them and normalize them. In particular, we can compute whether two rationals are equal (in finite time), which we can't do with reals.