Poset Definition Given a poset A, < and a set Sca ou∈ A is a upper bound of s if s≤ u for every s∈S
Poset . Definition . . Given a poset < A, ≤> and a set S ⊆ A. 1. u ∈ A is a upper bound of S if s ≤ u for every s ∈ S. 2. l ∈ A is a lower bound of S if l ≤ s for every s ∈ S. Yi Li (Fudan University) Discrete Mathematics February 24, 2014 6 / 15
Poset Definition Given a poset A, < and a set Sca u∈ A is a upper bound of s if s≤ u for every s∈S. l∈ A is a lower bound of s if l≤ s for every s∈S
Poset . Definition . . Given a poset < A, ≤> and a set S ⊆ A. 1. u ∈ A is a upper bound of S if s ≤ u for every s ∈ S. 2. l ∈ A is a lower bound of S if l ≤ s for every s ∈ S. Yi Li (Fudan University) Discrete Mathematics February 24, 2014 6 / 15
Poset Definition Given a poset A, < and a set Sca
Poset . 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 ′ for any other upper bound u ′ of S. 2. 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 GLB. Yi Li (Fudan University) Discrete Mathematics February 24, 2014 7 / 15