Poset Definition Given a poset A, <> we can define o a is maximal if there does not exist b e A such that a< b e a is minimal if there does not exist b e a such that a is greatest if for every b∈A, we have b≤a a is least if for every b∈A, we have a≤b.Poset Definition Given a poset < A, ≤>, we can define: 1 a is maximal if there does not exist b ∈ A such that a ≤ b. 2 a is minimal if there does not exist b ∈ A such that b ≤ a. 3 a is greatest if for every b ∈ A, we have b ≤ a. 4 a is least if for every b ∈ A, we have a ≤ b. Yi Li (Fudan University) Discrete Mathematics February 28, 2012 5 / 15