Bounded Set

Definition

Let $S$ be a nonempty subset of $\mathbb{R}$ ($S\ne \varnothing ,S\subseteq \mathbb{R}$)

1. If $\exists u\in \mathbb{R}\ni s\le u,\forall s\in S$, then we say $S$ is bounded above
2. If $\exists u\in \mathbb{R}\ni s\ge u,\forall s\in S$, then we say $S$ is bounded below
3. $S$ is bounded if $S$ is bounded above and below