How do you show irrational number r uncountable? - Answers

To show that the set of Irrational Numbers is uncountable, you can use Cantor's diagonal argument. First, assume that the set of irrational numbers is countable and list them in a sequence. By constructing a new number that differs from each listed irrational number at a specific decimal place, you can demonstrate that this new number is also irrational and not in the original list, leading to a contradiction. Thus, the set of irrational numbers must be uncountable.