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==Intervals==
{{See also|Interval (mathematics)}}
A '''convex set''' in a poset ''P'' is a subset {{mvar|I}} of ''P'' with the property that, for any ''x'' and ''y'' in {{mvar|I}} and any ''z'' in ''P'', if ''x'' ≤ ''z'' ≤ ''y'', then ''z'' is also in {{mvar|I}}. This definition generalizes the definition of [[interval (mathematics)|interval]]s of [[real number]]s. When there is possible confusion with [[convex set]]s of [[geometry]], one uses '''order-convex''' instead of "convex".
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