There are an infinite number of Irrational Numbers.
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There are infiitelt many subsets of irrational numbers. One possible subset is the set of all positive irrational numbers.
No they are not. The numbers Pi and e are irrational and are not radicals. There are many others.
One possible set, out of infinitely many, is positive irrational numbers.
Irrational numbers are infinitely dense so that there are infinitely many irrational numbers between any to numbers. In fact, there are more irrational numbers between any two numbers than there are rational numbers in total!
No. There are infinitely many of both but the number of irrational numbers is an order of infinity greater than that for rational numbers.