The GLB & LUB of Two Elements: Non-Unique Possibilities?

[Gear300]

The greatest lower bound and least upper bound of two elements a, b in a lattice do not have to be unique, do they? It could be the case that two equivalent or non-comparable glb or lub exist, right?

 

[theorem4.5.9]

They are unique in a lattice. By definition (according to wikipedia) a lattice a po-set where any two elements have a unique glb and lub (or infimum and supremum respectively).

http://en.wikipedia.org/wiki/Lattice_(order )

 

[Gear300]

Thanks.

 

[dcpo]

In a poset the glb and lub must be unique by antisymmetry.