[fph]

There definitely are contexts in which it makes sense to define 0/0 = 0. Example: given a vector x and an approximation y to it, you wish to compute the "componentwise error" delta, i.e., the minimum positive number delta such that each entry of y is within relative error at most delta from the corresponding entry of x:

(1) abs(y_i - x_i) <= delta * abs(x_i) for each i.

This number can be computed as

(2) delta = max (abs(y_i - x_i) / abs(x_i)) over each i.

If you wish to allow zero entries in your vectors while keeping the equivalence between (1) and (2), you have to define 0 / 0 = 0.