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Is there more rational numbers then irrational?
No. There are infinitely many of both but the number of irrational numbers is an order of infinity greater than that for rational numbers.
Are there more rational numbers then irrational?
No. Although the count of either kind of number is infinite, the cardinality of irrational numbers is an order of infinity greater than for the set of rational numbers.
Are the sets of rational and irrational numbers equal?
No. Although there are infinitely many of either, there are more irrational numbers than rational numbers. The cardinality of the set of rational numbers is À0 (Aleph-null) while the cardinality of the set of irrational numbers is 2À0.
Why does pi go on forever?
Because it's an irrational number, and that's what "irrational" means. There are lots of other irrational numbers, like the base of the natural logarithm e or the square root of 2.In fact, there are more irrational numbers than rational numbers. A lot more.Infinitely more, even. There are an infinite number of rational numbers, but the infinite number of irrational numbers is a higher infinity than the infinity of rational numbers.
Is every real number rational?
No. The set of real numbers contains an infinitely more irrational numbers than rational numbers.
