Nekar Xenos <nek### [at] gmailcom> wrote:
> I imagined the complex set would have a larger "density" if you could call  
> it that. (Real numbers would have a larger "density" than integers)

You can uniquely map each complex number to each real number on a
one-to-one basis, which means that the set of complex numbers is as
big as the set of reals.

Likewise you can map each rational number to each natural number on
a one-to-one basis, which means that the set of rational numbers is as
big as the set of natural numbers. (There's actually a rather easy way
to do this enumeration. See if you can figure it out.)

Perhaps a bit surprisingly, there is no one-to-one mapping between
rational numbers and real numbers, which means that the set of real
numbers is larger than the set of rational numbers.

This last thing is quite curious given that, for example, between any
two real numbers there is an infinite amount of rational numbers, and
vice-versa. It feels like there should be the same amount...

-- 
                                                          - Warp

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