Let f(x) be a real-valued function and let a be a number in the domain of f(x). If lim_(x->a) f(x) = L!=f(a), where L is a real number, then f(x) has a removable discontinuity at a. A removable discontinuity can be "fixed" by defining a new function g(x) so that lim_(x->a) g(x) = L = g(a). That is, the new function g(x) = piecewise f(x) L for x!=a for x = a is continuous at a.