Continuity versus Darboux property

A real function defined on a interval I is said to have the Darboux (or intermediate value) property if, whenever a and b are from I and c is any number between f(a) and f(b) there exists a number x (depending of c) such that f(x)=c. Introducing the Darboux rectangle this reformulate as follows: whenever a and b are from I, each parallel segment to x'x axis in the Darboux rectangle intersect the graphic of f.

 

Doru Paunescu

 
Resource Type
Activity
Tags
continuity  continuous  darboux  function  property 
Target Group (Age)
19+
Language
English (United Kingdom)
 
 
 
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