Darren New <dne### [at] sanrrcom> wrote:
> Orchid XP v8 wrote:
> > Darren New wrote:
> > 
> >> Map each real number to a positive integer.
> > 
> > Um... like, how? There's more of them...

> Yes. That's the point.  Assume you do that. Then construct a real not on 
> the list.  Obviously, your assumption that it was possible to do that 
> was wrong.

  It kind of "makes sense" that there are "more" reals than integers.
What is more unintuitive is that the amount of rational numbers is the
same as the amount of integers.

  (Curiously, to a mathematician it's the other way around: The latter
fact is quite intuitive, but the former is puzzling. Some even go as
far as half-jokingly saying that "there just can't be more reals than
integers, it doesn't make sense; there would be too many".)

-- 
                                                          - Warp

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