bracket

An interval [a, b] known to contain a root because f(a) and f(b) have opposite signs.

A bracket for a continuous function $f$ is an interval $[a,b]$ with $f(a)$ and $f(b)$ of opposite sign. The Intermediate Value Theorem then guarantees at least one root of $f$ inside $(a,b)$ . A bracketing method (bisection, the method of false position) always replaces one endpoint of a current bracket with a new point that keeps the bracket valid, so it never loses track of a root it has already boxed in.

Examples

$[1,2]$ is a bracket for $f(x)=x^3-x-2$ since $f(1)=-2<0$ and $f(2)=4>0$ .