Intermediate Value Theorem

  • Thread starter icystrike
  • Start date
  • #1
446
1

Homework Statement


Let f : [0; 1] -> [0; 1] be continuous on [0; 1]. Prove that there exists C [tex]\epsilon [0; 1][/tex] such
that f(c) = c.


Homework Equations





The Attempt at a Solution



I've manage to prove this by having an extra cont. function g(x)=f(x)-x .. But im looking for easier proof
 

Answers and Replies

  • #2
22,129
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Sorry, that's the easiest proof available :smile:
 
  • #3
446
1
Sorry, that's the easiest proof available :smile:

Is it one of the common proof and example when they conduct lesson on IVT?
 
  • #4
22,129
3,297
Yes, this is one of the common examples when discussing the IVT. There are other proofs however, but these are quite complicated (see Brouwers fixed point theorem)
 
  • #5
446
1
Thank you! Greatly appreciate ur time =D
 

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