From owner-qed Thu Sep 1 12:15:34 1994 Received: from localhost (listserv@localhost) by antares.mcs.anl.gov (8.6.4/8.6.4) id MAA02019 for qed-out; Thu, 1 Sep 1994 12:13:24 -0500 Received: from cats.ucsc.edu (root@cats-po-1.UCSC.EDU [128.114.129.22]) by antares.mcs.anl.gov (8.6.4/8.6.4) with ESMTP id MAA02014 for ; Thu, 1 Sep 1994 12:13:19 -0500 From: beeson@cats.UCSC.EDU Received: from si.UCSC.EDU by cats.ucsc.edu with SMTP id KAA02909; Thu, 1 Sep 1994 10:13:13 -0700 Received: by si.UCSC.EDU (8.6.9/4.7) id KAA26302; Thu, 1 Sep 1994 10:13:07 -0700 Date: Thu, 1 Sep 1994 10:13:07 -0700 Message-Id: <199409011713.KAA26302@si.UCSC.EDU> To: dahn@mathematik.hu-berlin.de, qed@mcs.anl.gov Subject: intermediate value theorem Sender: owner-qed@mcs.anl.gov Precedence: bulk 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.