Intermediate value property
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A real function is said to have the intermediate value property on an interval ![$[a, b]$](http://latex.artofproblemsolving.com/d/a/2/da2e551d2ca2155b8d8f4935d2e9757722c9bab6.png)
if, for each value 
between 
and 
, there is some 
such that 
. 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.
