## You are here

HomeBolzano's theorem

## Primary tabs

# Bolzano’s theorem

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

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

###### Theorem.

If a real function $f$ is continuous on a closed interval $I$ 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 $f(x)=0$.

Related:

PolynomialEquationOfOddDegree, Evolute2, ExampleOfConvergingIncreasingSequence

Type of Math Object:

Theorem

Major Section:

Reference

Parent:

Groups audience:

## Mathematics Subject Classification

26A06*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections