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I need to prove that $\mathbb{R}\setminus\mathbb{Q}$ is countable or uncountable. I believe it is uncountable. I am not sure how to prove it. $\mathbb{R}$ is known to be uncountable and $\mathbb{Q}$ is countable. By reason when I take the difference of the two it would be uncountable. How do I prove this?

MattAllegro
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1 Answers1

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If $\mathbb{R} \setminus \mathbb{Q}$ is countalbe, then $\mathbb{R}$ is countable. A contradiction.

user1123
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