episciences.org_2638_1634928311
1634928311
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Logical Methods in Computer Science
1860-5974
07
14
2020
Volume 16, Issue 3
Interpolating Between Choices for the Approximate Intermediate Value
Theorem
Matthew
Frank
This paper proves the approximate intermediate value theorem, constructively
and from notably weak hypotheses: from pointwise rather than uniform
continuity, without assuming that reals are presented with rational
approximants, and without using countable choice. The theorem is that if a
pointwise continuous function has both a negative and a positive value, then it
has values arbitrarily close to 0. The proof builds on the usual classical
proof by bisection, which repeatedly selects the left or right half of an
interval; the algorithm here selects an interval of half the size in a
continuous way, interpolating between those two possibilities.
07
14
2020
2638
arXiv:1701.02227
10.23638/LMCS-16(3:5)2020
https://lmcs.episciences.org/2638