Darren New <dne### [at] sanrrcom> wrote:
> Stuff like proofs that the number of real numbers 0 <= N < 1 is larger 
> than the number of positive integers.

> Map each real number to a positive integer. Now for each number, take 
> the real number whose first digit differs from the first digit of the 
> first real, whose second digit differs from the second digit of the 
> second real, etc. You've just constructed a real which is, by 
> construction, not on your list that maps all real numbers to integers.

  I think that the concept you are trying to explain could become clearer
if you also prove why the amount of rational numbers between 0 and 1 is
the *same* as the amount of integers. (In other words, each rational
number can be uniquely mapped to an integer, and there are no rational
numbers that can't be.)

-- 
                                                          - Warp

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