The term “continuous” describes the property of a function which maps “close” points of the domain into “close” points of the codomain. If a function is continuous, the small changes in input variables result in small changes in output variables. Speaking informally, a real function of one real variable is continuous if we can draw it in one stroke, without lifting a pen from paper. A prerequisite for the definition of the concept of differentiability is that a function is continuous. The same assumption is assumed in many economic applications. The lack of this property has important economic consequences, as we illustrate by presenting some applications of continuity to problems in economics.