Prove that the set of irrational numbers in [0,1] is not countable

Chaya Galloway 2021-02-25 Answered
Prove that the set of irrational numbers in [0,1] is not countable
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faldduE
Answered 2021-02-26 Author has 109 answers
It is known that the set of rational numbers are countable.
Union of rational numbers and irrational numbers gives the real numbers.
So [0,1]=Q[0,1]RQ[0,1]
Since Q[0,1] is countable and [0,1] is not countable.
So the only possibility is that RQ[0,1] is uncountable.
Hence, the set of irrational numbers in [0,1] is not countable.
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