Bolzano’s theorem

A continuous functionMathworldPlanetmathPlanetmath can not change its sign ( without going through the zero.

This contents of Bolzano’s theorem may be formulated more precisely as the


If a real function f is continuous on a closed intervalMathworldPlanetmath I and the values of f in the end points of I have opposite ( signs, then there exists a zero of this function inside the interval.

The theorem is used when using the interval halving method for getting an approximate value of a root of an equation of the form  f(x)=0.

Title Bolzano’s theorem
Canonical name BolzanosTheorem
Date of creation 2013-03-22 15:39:06
Last modified on 2013-03-22 15:39:06
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 5
Author pahio (2872)
Entry type Theorem
Classification msc 26A06
Related topic PolynomialEquationOfOddDegree
Related topic Evolute2
Related topic ExampleOfConvergingIncreasingSequence