Lower bound
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Needs fleshing out, a few references and a terminology section would be good
Contents
Definition
Let [ilmath](X,\preceq)[/ilmath] be a poset and let [ilmath]A\in\mathcal{P}(X)[/ilmath] be any subset of [ilmath]X[/ilmath]. An element [ilmath]b\in X[/ilmath] is an lower bound of [ilmath]A[/ilmath] if[1]:
- [ilmath]\forall a\in A[b\preceq a][/ilmath].
Equivalently, a subset [ilmath]A\in\mathcal{P}(X)[/ilmath] has a lower bound if:
- [ilmath]\exists b\in X\forall a\in A[b\preceq a][/ilmath] - "if there exists a lower bound."
Terminology
TODO: Things like "bounded below" and such
See also
- Infimum - the greatest lower bound of a set.
- Upper bound - the dual concept.
- Supremum - the lowest upper bound
References
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