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To: dahn@mathematik.hu-berlin.de, qed@mcs.anl.gov
Subject: intermediate value theorem
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Just to set a detail straight:  the intermediate value theorem for 
polynomials (indeed for real-analytic functions) can be proved without 
recourse to set theory, and even constructively proved.  See the discussion
on page 11 of my book, Foundations of Constructive Mathematics.
   Of course, G\"odel's theorem shows us that it WILL happen in 
general that there are theorems whose proofs require concepts not 
involved in the statement of the theorem.  But the intermediate 

value theorem isn't one of those theorems.