What is infinity squared?

Georg Cantor was the mathematian I was thinking about. He defined the 'aleph numbers' where aleph null is the cardinality of the set of all natural numbers.

I think I know where you're going with this. Different sets of numbers can be represented to have an "infinite" number of values, although sets can be compared to have more or less values than each other.

For example, consider the number of integers that exist (infinity) and the number of rational numbers that exist (infinity). Although they are both infinite amounts, there are certainly more rational numbers than integers since there is an infinite amount of rational numbers just between 0 and 1.

For this reason, we can do arithmetic with "infinities" that describe sets of numbers. Other than that, we cannot use infinity itself as a value.

I wrote a blog article about infinity and it can be found here: http://primedrive.blogspot.com/2009/05/infinity.html