The Converse of the Intermediate Value Theorem: From Conway to Cantor to Cosets and Beyond
The Converse of the Intermediate Value Theorem: From Conway to Cantor to Cosets and Beyond
The classical Intermediate Value Theorem (IVT) states that if $f$ is a continuous real-valued function on an interval $[a,b]\subseteq\mathbb{R}$ and if $y$ is a real number strictly between $f(a)$ and $f(b)$, then there exists a real number $x\in(a,b)$ such that $f(x)=y$. The standard counterexample showing that the converse of the …