1
$\begingroup$

Possible Duplicate:
Are there many more irrational numbers than rational?

I read this article where it mentioned

Countably infinite means you can set up a one-to-one correspondence between the set in question and the set of natural numbers. It can be shown that no such relationship can be established between the set of real numbers and the natural numbers, thus the set of real numbers is not "countable", but it is infinite.

I am not sure why the real numbers cannot be put in a one to one correspondence with the natural numbers. Can anybody explain?

  • 0
    This has been asked thoroughly on this site.2012-10-07
  • 0
    http://math.stackexchange.com/questions/39269/how-does-cantors-diagonal-argument-work http://math.stackexchange.com/questions/180550/why-is-the-cardinality-of-irrational-numbers-greater-than-rational-numbers http://math.stackexchange.com/questions/141081/prove-that-the-open-interval-0-1-contains-uncountably-infinite-numbers and more.2012-10-07

3 Answers 3