I’ve only cited a small bit of a great article about infinity (on io9.com…). This is one of those mysterious topics which most people seem to think that they understand, but presents quite a few paradoxes when examined. When I was young this was a topic which led me to ask some questions which necessitated learning math.
In any case, go to the cited link, io9.com occasionally has some really great content, and this article may give you all of the information which may need on this subject.
A brief introduction to infinity
http://io9.com/5809689/a-brief-introduction-to-infinity
The notion of infinity is fundamentally beyond the human ability to comprehend, but that hasn’t stopped mathematicians from trying. So just what is infinity, and why is there more than one of them? And just what is infinity plus one?
Last week, we searched for the largest meaningful number in the universe, but all of these must of course pale in comparison to infinity. Mathematicians define "infinity" very strictly. But we’ll stick with a broader, everyday definition: Infinity covers any number that isn’t finite. Now, without further ado, let’s expand our minds and tiptoe towards infinity.
The Beginning of Infinity
In order to talk about infinity, we first have to find a way to define it mathematically. That isn’t an easy task – while the concept of infinity was known to the ancient Greeks, and it features prominently in the calculus of Isaac Newton and Gottfried Liebniz, infinity wouldn’t be rigorously defined until the late 1800s. Before that, it was just some vast, amorphous concept, more an artifact of certain mathematical operations than something worth understanding in its own right.
Indeed, many 19th century mathematicians found infinity to be vaguely distasteful, and they felt it had no place in serious mathematical discussion. At best, infinity was something for philosophers to discuss, and you can imagine the sort of disdain with which such pronouncements were made. It was in that context that Georg Cantor published the first proof of the existence of infinity in 1874.
