Let $A$ be a nonempty compact subset of $\mathbb{R}$ and $c \in \mathbb{R}$.
Prove that there exists a point $a$ in $A$ such that $| c-a | =\inf \{| c-x |: x \in A \}$?
Let $A$ be a nonempty compact subset of $\mathbb{R}$ and $c \in \mathbb{R}$.
Prove that there exists a point $a$ in $A$ such that $| c-a | =\inf \{| c-x |: x \in A \}$?