What Is Continuity? - Expii
We can understand continuity (or discontinuity) of a function at a point, in terms of limits. A function f(x) is continuous at x=a if the limit of f(x) as x approaches a is f(a). (A discontinuity usually refers to a point x=a where f is defined but not equal to the limit, but sometimes singularities -- points x=a where f is undefined -- are also counted as discontinuities.) A function is continuous on an interval (or some other set) if it is continuous at every single point of that interval (or set). Usually, the term continuous function refers to a function that is continuous everywhere on its domain.