Infinity is a number if we want it to be: we can do math in whatever kind of topological space we want, including ones with defined ∞, such as the one point compactifications of ℝ or ℂ, the latter of which has a nice wiki page: http://en.wikipedia.org/wiki/Riemann_sphere

As wikipedia says, “arithmetic with infinity does not obey all of the usual rules of algebra, and so the extended complex numbers do not form a field.” But they’re quite handy for some uses.