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单词 BolzanosTheorem
释义

Bolzano’s theorem


A continuous functionMathworldPlanetmathPlanetmath can not change its sign (http://planetmath.org/SignumFunction) 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 intervalMathworldPlanetmath I and the values of f in the end points of I have opposite (http://planetmath.org/Positive) 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.

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