Bolzano's Theorem

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

Bolzano's theorem states that if is a continuous function in the closed interval with and of opposite sign, then there is a in the open interval such that .

Contributed by: Julio Cesar de la Yncera (May 2008)
Open content licensed under CC BY-NC-SA


Details

Snapshot 1: The function is positive in the interval and therefore for all in .

Snapshot 2: The function is negative in the interval so for all in .

Snapshot 3: The function is positive for and negative for , therefore there is a in such that .


Snapshots



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send