May 2024
Intermediate to advanced
687 pages
18h 35m
English
Content preview from Discrete Mathematical Structures by Pearson
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Ordered Sets and Lattices 8-11
Example 3 Let A be the poset of non-negative real numbers with usual partial order less than or
equal to (≤ ). Then, 0 (zero) is the minimal element of A. There are no maximal elements.
Example 4 The poset of set of integers Z with usual partial order relation ≤ has no maximal and
no minimal elements.
8.6.2 Least Upper Bound or Supremum
Let (P, ≤ ) be a poset and let A ⊆ P. An element x is said to be least upper bound (LUB) of A or
supremum of A if x is an upper bound of A and x ≤ y for all upper bounds of A.
The LUB of a poset, if it exists, is unique.
Example 1 Let P = {a, b, c, d, e, f } and let ≤ be the relation ...
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