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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...
foundations of mathematics. ...1, where 0 is the empty set and 1 is the set consisting of 0 alone. Both definitions require an extralogical axiom to make them workâthe axiom of infinity, which postulates the existence of an infinite set. Since the simplest infinite set is the set of natural numbers, one cannot really say that arithmetic has been reduced to logic.