intermediate value theorem
beeson@cats.UCSC.EDU
Thu, 1 Sep 1994 10:13:07 -0700
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.