Search Results for ""

As Lagrange showed, any irrational number alpha has an infinity of rational approximations p/q which satisfy |alpha-p/q|<1/(sqrt(5)q^2). (1) Furthermore, if there are no ...

Define the "information function" to be I=-sum_(i=1)^NP_i(epsilon)ln[P_i(epsilon)], (1) where P_i(epsilon) is the natural measure, or probability that element i is populated, ...

The process of computing or obtaining an integral. A more archaic term for integration is quadrature.

Kakutani's fixed point theorem is a result in functional analysis which establishes the existence of a common fixed point among a collection of maps defined on certain ...

Let [a_0;a_1,a_2,...] be the simple continued fraction of a "generic" real number, where the numbers a_i are the partial quotients. Then the Khinchin (or Khintchine) harmonic ...

A problem related to the continuum hypothesis which was solved by Solovay (1970) using the inaccessible cardinals axiom. It has been proven by Shelah and Woodin (1990) that ...

A Liouville number is a transcendental number which has very close rational number approximations. An irrational number beta is called a Liouville number if, for each n, ...

For a real number x in (0,1), let m be the number of terms in the convergent to a regular continued fraction that are required to represent n decimal places of x. Then for ...

The problem in computational geometry of identifying the point from a set of points which is nearest to a given point according to some measure of distance. The nearest ...

Given a statistical distribution with measured mean, mode, and standard deviation sigma, the Pearson mode skewness is (mean-mode)/sigma. The function was incorrectly ...