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:
“Postmodernism is, almost by definition, a transitional cusp of social, cultural, economic and ideological history when modernism’s high-minded principles and preoccupations have ceased to function, but before they have been replaced with a totally new system of values. It represents a moment of suspension before the batteries are recharged for the new millennium, an acknowledgment that preceding the future is a strange and hybrid interregnum that might be called the last gasp of the past.”
—Gilbert Adair, British author, critic. Sunday Times: Books (London, April 21, 1991)
“In every election in American history both parties have their clichés. The party that has the clichés that ring true wins.”
—Newt Gingrich (b. 1943)
“The history of progress is written in the blood of men and women who have dared to espouse an unpopular cause, as, for instance, the black man’s right to his body, or woman’s right to her soul.”
—Emma Goldman (1869–1940)