# Math Help - Irrational Uncountability proof

1. ## Irrational Uncountability proof

To Prove: The set R (reals) - Q (rationals) of irrational numbers is uncountable.

How does one go about proving that the set of irrational numbers is uncountable? Does the cardinality come into play? Any help would be appreciated!

2. Originally Posted by jstarks44444
To Prove: The set R (reals) - Q (rationals) of irrational numbers is uncountable.

How does one go about proving that the set of irrational numbers is uncountable? Does the cardinality come into play? Any help would be appreciated!

First prove the reals $\mathbb{R}$ are uncountable, and then your question is immediate, as a countable union of

countable sets is countable, let alone a finite union.

Tonio