Definition:Bounded Below

Let $$\left({S; \le}\right)$$ be a poset.

A subset $$T \subseteq S$$ is bounded below in $$S$$ if:

$$\exists m \in S: \forall a \in T: m \le a$$

That is, there is an element of $$S$$ (at least one) such that precedes all the elements in $$T$$.

If there is no such element, then $$T$$ is unbounded below (in $$S$$).