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Date: Tue, 4 Mar 2014 14:02:01 +1100
Subject: Re: Working with the set of real numbers (was: Finding size of Variable)
From: Chris Angelico <rosuav@gmail.com>
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Xref: csiph.com comp.lang.python:67631

On Tue, Mar 4, 2014 at 1:45 PM, Albert van der Horst
<albert@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.

ChrisA