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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...
Like. âThere are infinite numbers between 0 and 1. There's .1 and .12 and .112 and an infinite collection of others. Of course, there is a bigger infinite set of numbers between 0 and 2, or between 0 and a million. Some infinities are bigger than other infinities. A writer we used to like taught us that. There are days, many of them, when I resent the size of my unbounded set.