[altrego99]

Because floor is a discontinuous function.

But you are right, what I meant is there is no way to define 0^0 maintaining continuity of the power function. Why is this important? Because power is a continuous function otherwise.

[anderskaseorg]

Similarly, there is no way to define floor(n) for integers n maintaining continuity of the floor function, even though floor is a continuous function otherwise. We still define floor(n) = n because the meaning of the floor function is more important than its continuity. And so it is with exponentiation at (0, 0).