Say we are trying to prove $$ 0\cdot n = 0 $$ By mathematical induction, we start with a base case of n = 1 $$ 0\cdot 1 = 0 $$ So now we assume our original formula is true, and try to prove a case for $n+1$. $$ 0\cdot (n+1) = 0\cdot n + 0\cdot 1 = 0 $$ Why can't we take the limit as n approaches infinity?

This would tell us that infinity times zero is equal to zero.