With my half-semester's worth of basic university level maths, I will tentatively make the argument that Solutions One, Two and Three are invalid. I base this on the fact that the mathematical smallprint has not been taken into account. That's right, in today's dodgey world even mathematics has smallprint.

The fundamental laws regarding variables being operated on by zero that are used in the the first to third solution have the condition that the variable itself can't be zero:
  • 0/x = 0 For all x where x != 0
  • x/x = 1 For all x where x != 0
  • x/0 = infinity for all x where x != 0

    So the only viable solution is Four, undefined. The damn thing's meaningless. There is probably more smallprint involving complex numbers but it's irrelevant (I hope) and I'll be damned if i know it. I'm also probably failing my course (Intro to Calculus and Linear Algebra) so by no means take this as the be all and end all.

    Bob9000 I believe you're idea follows the same idea of the proof that 1=2, which is obviously flawed in some way (Look if it isn't then well... I'll be more than happy to concede to you as the universe collapses on our heads.