Let $X$ be a metric space and $A \subseteq X$. The diameter of $A$ is
\[\diam A = \sup \{d(a, b) : a, b \in A\}.\]$A$ is bounded if $\diam A < \infty$.
Let $X$ be a metric space and $A \subseteq X$. The diameter of $A$ is
\[\diam A = \sup \{d(a, b) : a, b \in A\}.\]$A$ is bounded if $\diam A < \infty$.