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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...
An example is the set of real number s and its proper subset, the set of integers. In the 1800s, Georg Cantor defined infinity in terms of the cardinalities of infinite sets. The cardinality of a set is the number of elements in the set. In this sense, the cardinality of the set of integers is smaller than the cardinality of the set of real numbers, even though both sets are infinite. The set of integers is denumerable (its elements can all be accounted for by means of a listing scheme), while the set of real numbers is not denumerable.