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{{Stub page|grade=A*|msg=Needs fleshing out, a few references and a terminology section would be good}}
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==Definition==
Let {{M|(X,\preceq)}} be a [[poset]] and let {{M|A\in\mathcal{P}(X)}} be any subset of {{M|X}}. An element {{M|b\in X}} is an ''upper bound'' of {{M|A}} if{{rLTFGG}}:
* {{M|\forall a\in A[a\preceq b]}}.
Equivalently, a subset {{M|A\in\mathcal{P}(X)}} has a ''upper bound'' if:
* {{M|\exists b\in X\forall a\in A[a\preceq b]}} - "if there exists a upper bound."
==Terminology==
{{Todo|Things like "bounded above" and such}}
==See also==
* [[Supremum]] - the ''lowest'' upper bound of a set.
* [[Lower bound]] - the [[dual (order theory)|dual]] concept.
** [[Infimum]] - the ''greatest'' lower bound.

==References==
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