Prove that the set of all irrational numbers is uncountable
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Prove that the set of irrational number is uncountable
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Answer...
The set R of all real numbers is the (disjoint) union of the sets of all rational and irrational numbers. ...
If the set of all irrational numbers were countable, then R would be the union of two countable sets, hence countable. Thus the set of all irrational numbers is uncountable.
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