Difference between revisions of "Intermediate value property"
m (latex rendering) |
(Reverted edits to remove spam) |
||
| (3 intermediate revisions by 3 users not shown) | |||
| Line 1: | Line 1: | ||
| − | + | 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. | |
| − | + | The simplest, and most important, examples of functions with this property are the [[continuous function]]s. | |
| − | + | {{stub}} | |
Latest revision as of 16:12, 13 November 2024
A real function is said to have the intermediate value property on an interval ![$[a, b]$](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.
This article is a stub. Help us out by expanding it.
