Quote:
There do exist different types of infinity. This distinction is sort of hard to think about until it's explained. There are enumerable infinities and then there are non-countable infinities. The sequence of natural numbers is an enumerable infinity; if we sat down for an infinite length of time we could count from 1 to infinity. The number of points between 0 and 1 on the number line, however, is uncountably infinite. There is no way given an infinite length of time we could count the points. Where would we start? Pick a point and I can find another one closer to 0 than the one you picked. We say that uncountable infinite items are much larger than countable infinite items. The number of points between 0 and 1 on then number line is much greater than the size of the set of the natural numbers. I hope this helps; infinity is a hard subject to nail down.
Here's a quote you might enjoy:
"Infinity is like a stuffed walrus I can hold in the palm of my hand. Don't do anything with infinity you wouldn't do with a stuffed walrus."
-Dr. Fletcher
Va. Polytechnic Inst. and St. Univ.
(i.e., don't use it as a number)