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 $\diam A<\infty$.