Editing Complete lattice (section)

=== Complete semilattices ===
The terms ''complete [[meet-semilattice]]'' or ''complete [[join-semilattice]]'' is another way to refer to complete lattices since arbitrary meets can be expressed in terms of arbitrary joins and vice versa (for details, see [[completeness (order theory)|completeness]]). 

Another usage of "complete meet-semilattice" refers to a meet-semilattice that is [[bounded complete]] and a [[complete partial order]]. This concept is arguably the "most complete" notion of a meet-semilattice that is not yet a lattice (in fact, only the top element may be missing).

See [[semilattice]]s for further discussion between both definitions.