Hmmm...In my math classes infinity was defined as not a number, but more or less as a vector, or direction.
To put it this way, if you have a function that approaches infinity (take a limit of sorts), you will know that as x (or any variable) increases, there will be a proportionality function that is the actual function that describes how the other variable increases.
For example, the function f(x)=1/x, as x approaches 0 from either side, the function f(x) will increase exponentially with each iteration. In that sense, infinity can never be reached because of the computational power of both the human mind or the graphing utility. Therefore, we define infinity to be a dirction to which a function approaches.
Sorry if that made no sense, I just woke up
