Working with the set of real numbers (was: Finding size of Variable)

Rustom Mody rustompmody at gmail.com
Tue Mar 4 04:13:58 CET 2014


On Tuesday, March 4, 2014 8:32:01 AM UTC+5:30, Chris Angelico wrote:
> On Tue, Mar 4, 2014 at 1:45 PM, Albert van der Horst 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.

See

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/cfINTRO.html#sqrts




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