In contrast, the function denoting the amount of money in a bank account at time would be considered discontinuous, since it "jumps" at each point in time when money is deposited or withdrawn. ==History== A form of the epsilon–delta definition of continuity was first given by Bernard Bolzano in 1817.
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.
Eduard Heine provided the first published definition of uniform continuity in 1872, but based these ideas on lectures given by Peter Gustav Lejeune Dirichlet in 1854. ==Real functions== ===Definition=== A real function, that is a function from real numbers to real numbers, can be represented by a graph in the Cartesian plane; such a function is continuous if, roughly speaking, the graph is a single unbroken curve whose domain is the entire real line.
Eduard Heine provided the first published definition of uniform continuity in 1872, but based these ideas on lectures given by Peter Gustav Lejeune Dirichlet in 1854. ==Real functions== ===Definition=== A real function, that is a function from real numbers to real numbers, can be represented by a graph in the Cartesian plane; such a function is continuous if, roughly speaking, the graph is a single unbroken curve whose domain is the entire real line.
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.
All text is taken from Wikipedia. Text is available under the Creative Commons Attribution-ShareAlike License .
Page generated on 2021-08-05