S pecial Lattice Definition a lattice L is complete if any finte or infinite) subset A=aili e I has a least upper bound Uierai and a greatest lower bound∩∈ra Definition A lattice L is bounded if it has a greatest element 1 and a least element 0 Theorem Finite lattice L=al,., an is boundedSpecial Lattice Definition A lattice L is complete if any(finte or infinite) subset A = {ai |i ∈ I} has a least upper bound ∪i∈Iai and a greatest lower bound ∩i∈Iai . Definition A lattice L is bounded if it has a greatest element 1 and a least element 0. Theorem Finite lattice L = {a1, . . . , an} is bounded. Yi Li (Fudan University) Discrete Mathematics March 6, 2012 8 / 1