Are there more rational or irrational numbers? [duplicate]
On the number line, are there more rational numbers or irrational numbers? I was told that there are equally many rational and irrational numbers. Is this correct? How could we prove that?
Solution 1:
Hint The cardinality of the rational numbers, $|\Bbb Q|)$, is countable, but the cardinality of the real numbers, $|\Bbb R|$, is uncountable. How many irrational numbers $|\Bbb R \setminus \Bbb Q|$ must there be?