Bounded-complete partially ordered set
= Bounded-complete partially ordered set
{title2=$\sup S\text{ exists whenever }S\text{ has an upper bound}$}
Every subset having an <upper bound> has a <least upper bound>. If the empty subset is included, a nonempty such <partially ordered set> has a <least element>. This condition differs from a <directed-complete partial order>: a <directed set> need not have an <upper bound>.