Orchid XP v8 wrote:
>> Map each real number to a positive integer.
> 
> Um... like, how? There's more of them...

	What he meant to say was that no matter how you map integers to real 
numbers, one can construct a real number that has no integer mapped to it.

Me: There's no way to make a 1-1 correspondence between reals and integers.

You: Yes there is.

Me: I defy you to provide me with such a mapping.***

You: OK. How about this one?

Me: (Using Darren's recipe) - here's a real number that isn't mapped to 
an integer.

*** Not a mathematically sound argument. In mathematics, you can prove 
the existence of certain sets, and you can also prove that you can never 
   explicitly exhibit those sets (i.e. you can *only* show they exist - 
it is mathematically impossible to demonstrate them, though). So an 
argument that shows one cannot exhibit/construct a certain set does not 
imply that they don't exist.

Some day I have to formally learn how that is.

-- 
"Auntie Em: Hate Kansas. Hate You. Took Dog. -Dorothy."


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