Poset Definition Given a poset A, < and a set Sca o u is a least upper bound of S, (LUB(S)), if u is the upper bound of s and u u' for any other er bound u of o l is a greatest lower bound of S, GLB(S)), if l is the upper bound of s and l'<l for any other lower bound l' of s Theorem A poset has at most one lUb or GLBPoset Definition Given a poset < A, ≤> and a set S ⊆ A. 1 u is a least upper bound of S, (LUB(S)), if u is the upper bound of S and u ≤ u 0 for any other upper bound u 0 of S. 2 l is a greatest lower bound of S, (GLB(S)), if l is the upper bound of S and l 0 ≤ l for any other lower bound l 0 of S. Theorem A poset has at most one LUB or GLB. Yi Li (Fudan University) Discrete Mathematics February 28, 2012 7 / 15