Since there is a rational number between any two irrational

Dania Mueller

Dania Mueller

Answered question

2022-06-13

Since there is a rational number between any two irrational numbers, so can we say that rational number and irrational number have the same cardinality?

Answer & Explanation

Misael Li

Misael Li

Beginner2022-06-14Added 14 answers

No. Q is countable. Suppose that the irrational numbers have the same cardinality, then R Q is also countable. This gives

R = Q ( R Q ) is countable, a contradiction.

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