Solution
= Solution
{c}
The <infimum> of $A$ is its greatest <lower bound>: $\alpha=\inf A$ means that $\alpha\leq x$ for every $x\in A$, and that every <lower bound> $l$ of $A$ satisfies $l\leq\alpha$. The <supremum> is its least <upper bound>: $\beta=\sup A$ means that $x\leq\beta$ for every $x\in A$, and every <upper bound> $u$ satisfies $\beta\leq u$. The <completeness of the real numbers> ensures that both exist for a nonempty bounded <set> of <real numbers>.