Bounded below - Knowlpedia

A bounded below set is a subset $A\subseteq\mathbb R$ for which there exists $m\in\mathbb R$ such that $m\le x$ for every $x\in A$ ; such an $m$ is called a lower bound of $A$ .

Examples

$A=(0,1)$ is bounded below (for example, by $m=0$ ).
$A=\mathbb R$ is not bounded below.

Remarks

This notion uses the order axioms and is the basic hypothesis needed to define the infimum. A set can be bounded below without having a minimum.