Levels of infinity???

I was wondering, are there levels of infinity? For example; the even numbers 2,4,6,8.... go on for ever, as do the odd numbers 1,3,5,7...and so on. So is the entire set of numbers 1,2,3,4,5,6... twice as large as the set of even or odd numbers even though they both go on forever? Just wondering.

Well, to have many of your questions answered, you probably want to visit Dr. Math. Secondly, you should probably have this in the science and tech forum, since it is mathematical more than it is spiritual.

Disregarding formality, the answer is that many people believe that there are different sized infinities. An infinite number line is smaller than an infinite three dimensional volume. There is, of course, problems trying to determine what infinity is. There are a few different kinds of infinity, as I understand it. The main quality that seems to pop up is the idea of boundlessness. Although I question the nature of this definition for infinity, it does set a standard.

Infinity was originally defined by Georg Cantor. He believed that, "a collection is infinite, if some of its parts are as big as the whole." To the laymen, this doesn't mean much, but in the world of infinity the whole seems to remain undefined, yet its behavior can be somewhat predicted. Again, the case of a number line going to infinity is seen as going in one cardinal direction, therefore it has predictable qualities.

Infinity does not exclusively deal with numbers. Infinity can be thought of as x, x^2, sqrt(x), etc. To approach infinity means to have all possible values accounted for, or they are not in a complete solution set. The only point of trying to calculate infinity is to account for values that may seem unreasonable.

You could study this subject for most of your life and still only uncover a portion of its potential. Good luck.

[Edited on 20-10-2003 by Protector]

Yes the basic difference is countable sets versus uncountable sets. An infinite set is considered countable if a one to one relationship can be set up between that set and the integers (1, 2, 3, 4, ...). Certain rules become obvious. All finite sets are countable. Any subset of a countable set is countable. Examples of countable sets are the even numbers, the odd numbers, and believe it or not the rationals (1/3. etc.). The real number continum is the best example of an uncountable set. A one to one relationship between the reals and the integers cannot be generated.

I wasn't talking about numbers specifically. I was just using them as an example.

numbers and "frames" of numbers exist as measurable objects only in this "dimension"...

yet, divine numbers such as prime numbers create much of what you see, as well as the golden rule, and pi and phi...

math is filled with expressions of the "father of creation" and through life we can grow to appreciate all of his many "faces"

Well if you weren't talking about numbers, then there are indeed 12 levels of infiniti. The problem with explaining the 12 levels of infiniti is that it takes an infinite amount of time. You can see my problem here.

So what is bigger? infiniti, or infiniti + 1, or infiniti -1, or infiniti + infiniti, or infiniti times infiniti, or infiniti to the power of infiniti?