No, they can be as big as you like.
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All rational and irrational numbers are real numbers.
All irrational numbers are not rational.
All irrational numbers are real, but not all real numbers are irrational.
No. All irrational numbers are real, not all real numbers are irrational.
No, not at all. There are more irrational numbers between 1 and 2 than there are rational numbers in total!