Infinity doesn't have a value. It's an

ideal number. This means it does not occupy a point on the

real line. It occupies a position similar to that of the extra point in the

projective plane (the one at which parallel lines meet).

One way of visualising how this works is like this *(This was explained to me when I was jet-lagged out of my mind and still made some sense. it must be good.)*:

Imagine the complex plane as a flat plane in 3-dimensional space. Imagine a sphere resting on this plane so that the bottom of the sphere just touches the point representing zero. One can visualise a mapping from each point P on the plane to a point P' on the sphere. Simply draw a line from the top of the sphere I, through P. The other point at which IP cuts the sphere is P'.

Obviously there exists a P' for every P and there exists a P for every P' *except* I. The number which would map to I is infinity. As you can see, this explains why minus infinity equals plus infinity, something I never understood before.

I hope this helps people get a handle on infinity. It may make no sense at all, but hey, it's infinity, it never made sense in the first place.