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:
“A country grows in history not only because of the heroism of its troops on the field of battle, it grows also when it turns to justice and to right for the conservation of its interests.”
—Aristide Briand (1862–1932)
“To a surprising extent the war-lords in shining armour, the apostles of the martial virtues, tend not to die fighting when the time comes. History is full of ignominious getaways by the great and famous.”
—George Orwell (1903–1950)
“The only thing worse than a liar is a liar that’s also a hypocrite!
There are only two great currents in the history of mankind: the baseness which makes conservatives and the envy which makes revolutionaries.”
—Edmond De Goncourt (1822–1896)