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Report Abuse. Not only are they infinite, but they are uncountably infinite. That means the set of irrationals between 0 and 1 is larger than the set of all integers. Look up Georg Cantor on the internet. He proved all kinds of things about infinity. Source(s): http://en.wikipedia.org/wiki/Georg_Canto...
In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality of sets. The cardinality of a finite set is a natural number: the number of elements in the set. The transfinite cardinal numbers describe the sizes of infinite sets. Cardinality is defined in terms of bijective functions. Two sets have the same cardinality if, and only if, there is a one-to-one correspondence between the elements of the two sets. In the case of f