Problems caused by uming that 0/0 = 0, and that n/0 = infinity?

The Wikipedia article on division by zero mentioned that Brahmagupta umed 0/0 = 0, and Bhaskara II umed that n/0 = infinity if n did not equal 0. What are a few of the "paradoxes" and "algebraic absurdities" caused by these two umptions?