Carothers - Real Analysis
Chapter 1 - Calculus review
Exercise 1.1 : If $A$ is a nonempty subset of \mathbb{R} that is bounded below, show that $A$ has a greatest lower bound. That is, show that there is a number $m \in \mathbb{R}$ satisfying: (i) $m$ is a lower bound for $A$; and (ii) if $x$ is a lower bound for $A$, then $x < m$. [Hint: Consider the set $-A = \{-a : a \in A\}$ and show that $m = -\sup( -A)$ works.]
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