An alternative continuity concept is provided by Augustin-Louis Cauchy, who was inspired by the idea that every real number is the limit of the various rational sequences converging to it. A sequence of real numbers is a Cauchy sequence if the points in the sequence become eventually as close as desired to one another. The continuity of the real numbers is expressed by Cauchy completeness, the property that every Cauchy sequence converges to a limiting real number.
