X-Nico

2 unusual facts about Continuous function


Hyperbolic partial differential equation

\vec {f^j} \in C^1(\mathbb{R}^s, \mathbb{R}^s), j = 1, \ldots, d are once continuously differentiable functions, nonlinear in general.

Social value orientations

This conceptualization indicates that SVO is a continuous construct, since there is an infinite number of possible SVOs, because angular degrees are continuous.


Analogue electronics

Analogue electronics (or analog in American English) are electronic systems with a continuously variable signal, in contrast to digital electronics where signals usually take only two different levels.

Buridan's ass

The situation of Buridan's ass was given a mathematical basis in a 1984 paper by American computer scientist Leslie Lamport, in which Lamport presents an argument that, given certain assumptions about continuity in a simple mathematical model of the Buridan's ass problem, there will always be some starting conditions under which the ass will starve to death, no matter what strategy it takes.

Negligible function

Though the concepts of "continuity" and "infinitesimal" became important in mathematics during Newton and Leibniz's time (1680s), they were not well-defined until late 1810s.


see also

Convergence of Fourier series

It might be interesting to note that Jean-Pierre Kahane and Yitzhak Katznelson proved that for any given set E of measure zero, there exists a continuous function ƒ such that the Fourier series of ƒ fails to converge on any point

HLP

Homotopy lifting property, in algebraic topology, a technical condition on a continuous function from a topological space E to another one, B designed to support the picture of E "above" B