Bolzano's Root Point Theorem

,#analysis

Definition

Nullstellensatz von Bolzano

Bolzano's Zero Theorem

Let $f:[a,b]\to \mathbb{R}$ be a continuous function on the entire interval $[a,b]$ such that $f(a)<0$ and $f(b)>0$. Then $f$ has at least one root point in $(a,b)$, i.e., there exists a $c\in [a,b]$ with $f(c)=0$.