On Sunday, May 22, 2016 at 10:20:11 PM UTC+5:30, Jon Ribbens wrote: > On 2016-05-22, Chris Angelico wrote: > > Python's int and float types are both approximations to a > > non-representable type called a "real number". > > Sorry, I have to stop you there as the entire premise of your post is > clearly wrong. "int" is not "an approximation of real numbers", it's > a model of the mathematical concept "integers", and it's not an > approximation, and since the long/int unification you can't even > overflow it as I understand things (barring ridiculous situations like > running out of memory).
Well maybe Chris should have said (or meant to say?) In math: ℤ ⊆ ℝ whereas in programming int and float are disjoint types. So structurally the (int,float) type pair poorly approximates the (ℤ, ℝ) pair of math sets Doesnt mean I agree with > we can't perfectly represent real numbers or calculate with them, so we do > the best we can Floats are a grotesque travesty of ℝ At the least, interval arithmetic can help automatically do the numerical analysis for you. Then there are all kinds of rational approximations like continued fractions which are better than ℚ All the way to "computable real numbers" We're stuck with them because that's the hardware we've got. Nothing intrinsic or necessary about it -- https://mail.python.org/mailman/listinfo/python-list
