I am not a mathematician, but I know that at least in standard mathematics it is fairly ill-advised to treat infinity implicitly as a number. Doing so can result in various contradictions (two different seemingly valid solutions to a problem). It should be thought of as a property of a process, i.e. for any number x you can change the process so that it results in a number greater than x. One example of infinity might be: "Think of a number which you are allowed to change after each number I suggest. If for any number I suggest you change it for a bigger one, then what you think of is infinity."

Chapter 15: Paradoxes of probability theory in Jaynes's "Probability Theory: Logic of Science" is a great reading on the topic (you can find a pdf easily on google). It starts with a quote from Gauss:

"I protest against the use of infinite magnitude as something accomplished, which is never permissible in mathematics. Infinity is merely a figure of speech, the true meaning being a limit." -- C. F. Gauss

Anyway, there are plenty of theories in mathematics which use infinity implicitly, but one should perhaps be cautious.