Q:

Convex hull of one point in $\mathbb{R}^{2}$

Let $S\in\mathbb{R}^{2}$ and let the size of $|S|=1$. If $x\in S$ then what is the convex hull of $S$?  Is it $\{x\}$ or is it an empty set?  Thank you. 

A:

By the definition of Convex Hull of a set S, it is the smallest convex set containing all points of S and since a singleton set is convex itself, thus convex hull of $\{x\}$ is $\{x\}$ itself.