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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...
Intuitive picture. A finite set is like a deck of cards in a box. You can reach in and pull out another card N times, but the N+1st time you won't get a card. Not complicated, but you do have to keep track of N. An infinite set is like a box that always has another card.