Intermediate value property

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A real function is said to have the intermediate value property on an interval $[a, b]$ if, for each value $v$ between $\displaystyle f(a)$ 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.