Are There More Real Numbers Than Rational Numbers Without Complex Set Theory?

[dmatador]

I am trying to figure out a way to prove this without using much set theory (i know that the rationals are countable and the reals are not). is there a way to show that there are more reals than rationals in a more straightforward proof?

 

[LCKurtz]

You don't like the Cantor diagonal proof?

http://en.wikipedia.org/wiki/Cantor's_diagonal_argument