In article <mailman.7687.1393902132.18130.python-l...@python.org>, Chris Angelico <ros...@gmail.com> wrote: >On Tue, Mar 4, 2014 at 1:45 PM, Albert van der Horst ><alb...@spenarnc.xs4all.nl> wrote: >>>No, the Python built-in float type works with a subset of real numbers: >> >> To be more precise: a subset of the rational numbers, those with a >> denominator >> that is a power of two. > >And no more than N bits (53 in a 64-bit float) in the numerator, and >the denominator between the limits of the exponent. (Unless it's >subnormal. That adds another set of small numbers.) It's a pretty >tight set of restrictions, and yet good enough for so many purposes. > >But it's a far cry from "all real numbers". Even allowing for >continued fractions adds only some more; I don't think you can >represent surds that way.
Adding cf's adds all computable numbers in infinite precision. However that is not even a drop in the ocean, as the computable numbers have measure zero. A cf object yielding its coefficients amounts to a program that generates an infinite amount of data (in infinite time), so it is not very surprising it can represent any computable number. Pretty humbling really. > >ChrisA Groetjes Albert -- Albert van der Horst, UTRECHT,THE NETHERLANDS Economic growth -- being exponential -- ultimately falters. albert@spe&ar&c.xs4all.nl &=n http://home.hccnet.nl/a.w.m.van.der.horst -- https://mail.python.org/mailman/listinfo/python-list
