Difference between revisions of "Intermediate value property"

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A [[real]] [[function]] is said to have the '''intermediate value property''' on an [[interval]] <math>[a, b]</math> if, for each value <math>v</math> between <math>f(a)</math> and <math>f(b)</math>, there is some <math>c \in (a, b)</math> such that <math>f(c) = v</math>.  Thus, a function with the intermediate value property takes all intermediate values between any two points.
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The simplest, and most important, examples of functions with this property are the [[continuous function]]s.
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Latest revision as of 16:12, 13 November 2024

A real function is said to have the intermediate value property on an interval $[a, b]$ if, for each value $v$ between $f(a)$ and $f(b)$, there is some $c \in (a, b)$ such that $f(c) = v$. Thus, a function with the intermediate value property takes all intermediate values between any two points.

The simplest, and most important, examples of functions with this property are the continuous functions.

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