Uncountable

[reddog843]

Prove that the set of irrational numbers is uncountable.

[HallsofIvy]

Using WHAT basis?

If you are allowed to use the fact that the set of real numbers is uncountable, it is trivial: the union of two countable sets is countable.

If not then it is probably simplest to first prove that the set of real numbers is uncountable, by Cantor's argument, then apply the above.

[Metal70]

You could prove it by showing that there does not exist a surjective function f:N->I, where N is the set of naturals and I the set of irrationals.