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

[Chris Angelico]

On Tue, Mar 4, 2014 at 2:13 PM, Rustom Mody <rustompmody at gmail.com> wrote:
>> 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

That's neat, didn't know that. Is there an efficient way to figure
out, for any integer N, what its sqrt's CF sequence is? And what about
the square roots of non-integers - can you represent √π that way? I
suspect, though I can't prove, that there will be numbers that can't
be represented even with an infinite series - or at least numbers
whose series can't be easily calculated.

ChrisA