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The distance between any two terms $b_n$ and $b_m$ (with $m > n$) is bounded by the length of the interval $[a_n, b_n]$. Because the bisection method halves the interval length at each step, this distance is bounded by $\left(\frac{1}{2}\right)^{n-1}|b_1 - a_1|$.

Conditions: $m > n \in \mathbb{N}$.; The sequences $(a_n)$ and $(b_n)$ are constructed via the bisection method.; $b_n$ is an upper bound and $a_n$ is a lower bound for the set $M$.

The distance between any two terms $b_n$ and $b_m$ (with $m > n$) is bounded by the length of the interval $[a_n, b_n]$. Because the bisection method halves the interval length at each step, this distance is bounded by $\left(\frac{1}{2}\right)^{n-1}|b_1 - a_1|$.

Conditions: $m > n \in \mathbb{N}$.; The sequences $(a_n)$ and $(b_n)$ are constructed via the bisection method.; $b_n$ is an upper bound and $a_n$ is a lower bound for the set $M$.