[[Metric space]]
# Diameter of a set

In a metric space $(X,d)$ the **diameter** $\mathrm{diam}(Y)$ of a subset $Y \sube X$ is the [[Poset#^sup|supremum]] of the difference between any two points in $Y$, #m/def/anal i.e.
$$
\begin{align*}
\mathrm{diam}(Y) = \sup \{ d(x,y) : x,y \in Y \}
\end{align*}
$$


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