Addition: Multiplication: Infinity + Finite = Infinity Infinity x Infinity = Infinity Infinity + Infinity = Infinity Infinity x Finite = Infinity, but Infinity x 0 is undefined Infinity + -Infinity can be absolutely anything finite or not Infinity x -Infinity = -Infinity -Infinity + Finite = -Infinity -Infinity x Finite = -Infinity, with the same exception for 0 as before -Infinity + -Infinity = -Infinity -Infinity x -Infinity = Infinity Subtraction: Same as addition, with u-v treated as u+(-v): where -(Infinity) = -Infinity -(-Infinity) = Infinity Division: Same as multiplication, with u/v treated as u x (1/v): where 1/(-Infinity) = -0 1/(Infinity) = +0 1/(-0) = -Infinity 1/(+0) = Infinity You'll need to make the distinction between +0 and -0, if you're going to say anything useful about division with infinity. These rules are made in such a way that all the properties (+,x,-,/) will remain true when infinite limits are included. It is possible for a limit to be infinite without its positive or negative sign being determined. This limit will represent the unsigned infinity. Its negative is itself and its reciporical is 0 (without the + or - sign). You'll need to use all three kinds of infinity. Much of Calculus is devoted to resolving those limits involving the undefined operations above, like Infinity - Infinity, Infinity x 0, Infinity/Infinity There is a theory of infinitesimals based on what is known as Non-Standard Analysis. Its content is completely equivalent to Calculus. In fact, it is a reformulation of Calculus that matches very closely the original formulation of Calculus as a calculation system for infinite and infinitesimal numbers.