Definition:Bounded/Ordered Set

Definition

Let $\left({S, \preceq}\right)$ be a poset.

Let $T \subseteq S$ be both bounded below and bounded above in $S$.

Then $T$ is bounded in $S$.

Sources

• James M. Hyslop: Infinite Series (1942): $\S 3$
• Seth Warner: Modern Algebra (1965)... (previous)... (next): $\S 14$
• K.G. Binmore: Mathematical Analysis: A Straightforward Approach (1977)... (previous)... (next): $\S 2.2$