why 0/0 is undefined:
if 0/0 had a value, it would either be 0 (0 divided by a non-zero number is 0) or 1 (a number divided by itself is 1,) but by giving a non-algebraic expression several solutions, contradictions arrive, breaking the fundamentals of math (if 0/0=0 and 0/0=1, does 1=0?)