2010-03-14, 05:12 AM
If you're stuck on the fact that 0.999... can't be equal to 1 because it forever gets closer and closer and eventually has to stop sometime, think of it this way.
You have a number which is infinite. It's a number that is forever increasing and never, ever stops increasing.
In a sense, what you're doing is stopping the number at 1,394,194,103 and saying, "See? It stops there. So it can't possibly get any closer to infinity." But it can get closer. By stopping an infinite number at a finite number, you are contradicting what infinity really is. The whole point of infinity is that it never stops increasing.
You have a number which is infinite. It's a number that is forever increasing and never, ever stops increasing.
In a sense, what you're doing is stopping the number at 1,394,194,103 and saying, "See? It stops there. So it can't possibly get any closer to infinity." But it can get closer. By stopping an infinite number at a finite number, you are contradicting what infinity really is. The whole point of infinity is that it never stops increasing.
