### Are there more rational number than irrational numbers?

There are more irrational numbers than rational numbers. The

rationals are countably infinite; the irrationals are uncountably

infinite. Uncountably infinite means that the set of irrational

numbers has a cardinality known as the “cardinality of the

continuum,” which is strictly greater than the cardinality of the

set of natural numbers which is countably infinite. The set of

rational numbers has the same cardinality as the set of natural

numbers, so there are more irrationals than rationals.