Definition:Bounded Below Mapping/Unbounded

This page is about Unbounded Below in the context of Mapping. For other uses, see Unbounded Below.

Definition

Let $f: S \to T$ be a mapping whose codomain is an ordered set $\struct {T, \preceq}$.

Then $f$ is unbounded below (in $T \ $) if and only if there exists no $L \in S$ such that:

$\forall x \in S: L \preceq \map f x$