Edit: Ok, I think I got my fallacy by reading the coments criticising that article abaut nullity. As I understood it it is perfectly posible to say x/0, but evrything is a solution to it, so it's just meaningless, along the lines of saying x=x, it's MORE meaningles than saying -∞<X<∞ because that excludes some nonreal numbers. A graph with divide by zero would be a solid square of ink.
Is this correct?
Hm... sort of. When you write x/0 = y, you get x = 0*y but x =/= 0. Basically, division by zero breaks the basic purpose of algebra (getting solutions to equations), so we leave it out. It's not about the meaninglessness of writing x/0, since that tends to ∞. It's about all the parts of math that it breaks and we'd really rather have around.
Saying -∞ < x < ∞ is fairly meaningful in all cases--it tells us we've got an arbitrary infinite set with certain characteristics defined. That kind of statement is the limiting factor one needs to begin a proper proof, since very rarely are things true for all numbers.
If we graphed the solutions to the equation x/0 = y, then yes, we'd get a solid block of ink... though in general, we just don't because the statement -∞ < x < ∞, -∞ < y < ∞ such that x/0 = y is kind of pointless, as outlined above. No matter what you do with it, it's universe-breaking.