An in Depth look into Infinity

Infinity is the biggest thing you can imagine, then imagine a lot more. Infinity is a number, however it is very different from any normal number like 1, 2, 10, or 5 million, it is infinitely larger than any of these. ¡§But how big is infinity?¡¨ That is one question that will never be answered completely. For now let¡¦s start out with some simpler concepts and we will grow to that more difficult one later.
Let¡¦s think about some sets that we know are infinitely large; the set of positive integers, the set of real numbers, the set of even integers, the set of rationals, and so on. We know a lot of sets that are infinitely large. In fact if we think hard enough, we can come up with infinitely many, infinitely large sets. We know the set of integers that are multiples of one, the set of integers that are multiples of two, of three, and of any other integer. But this still doesn¡¦t answer our question ¡§how big is infinity?¡¨ Is any one of these infinities larger...