History
A form of this epsilon-delta definition of continuity was first given by Bernard Bolzano in 1817. Preliminary forms of a related definition of the limit were given by Cauchy. Cauchy defined continuity of f as follows: an infinitely small increment of the independent variable x produces always an infinitely small increment change of f(x). Cauchy defined infinitely small quantities in terms of variable quantities, and his definition closely parallels the infinitesimal definition used today (see microcontinuity). The formal definition and the distinction between pointwise continuity and uniform continuity were first given by Bolzano in the 1830s but the work wasn't published until the 1930s. Heine provided the first published definition of uniform continuity in 1872, but based these ideas on lectures given by Dirichlet in 1854.
Read more about this topic: Continuous Function
Famous quotes containing the word history:
“We know only a single science, the science of history. One can look at history from two sides and divide it into the history of nature and the history of men. However, the two sides are not to be divided off; as long as men exist the history of nature and the history of men are mutually conditioned.”
—Karl Marx (1818–1883)
“In the history of the United States, there is no continuity at all. You can cut through it anywhere and nothing on this side of the cut has anything to do with anything on the other side.”
—Henry Brooks Adams (1838–1918)