/sci/ - Science & Math

Is this a mistake? If f(x) = 0 on [-1, 0) U (0, 1] and f(x) = 1 for x=0, why would lim x ->0 not exist?

I assume this is a consequence of the books limit definition, which says x can equal x0. But doesn't this mean limits are only defined for points in the domain if the function is continuous at that point?