Difference between revisions of "Lower bound"
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Latest revision as of 07:23, 20 May 2016
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Needs fleshing out, a few references and a terminology section would be good
Contents
[hide]Definition
Let (X,⪯) be a poset and let A∈P(X) be any subset of X. An element b∈X is an lower bound of A if[1]:
- ∀a∈A[b⪯a].
Equivalently, a subset A∈P(X) has a lower bound if:
- ∃b∈X∀a∈A[b⪯a] - "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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