 Though the concepts of "continuity" and "infinitesimal" became important in mathematics during Newton and Leibniz's time (1680s), they were not well-defined until the late 1810s.The first reasonably rigorous definition of "continuity" in mathematical analysis was due to Bernard Bolzano, who wrote in 1817 the modern definition of continuity.Later Cauchy, Weierstrass and Heine also defined as follows (with all numbers in the real number domain formula_5)