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You can choose an irrational number to be either greater or smaller than any given rational number.

On the other hand, if you mean which set is greater: the set of Irrational Numbers is greater. The set of rational numbers is countable infinite (beth-0); the set of irrational numbers is uncountable infinite (more specifically, beth-1 - there are larger uncountable numbers as well).

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Q: Which one is more irrational or rational?
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