April 2024
Intermediate to advanced
832 pages
29h 31m
English
Content preview from Design and Analysis of Algorithms
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638 Design and Analysis of Algorithms
A.10.7 Upper Bounds and Lower Bounds
Let (A, R) be a poset. Let B be a subset of A.
An element x in A is called an upper bound of B if yRx for every y in B.
An element x in A is called a lower bound of B if xRy for every y in B.
An upper bound x of B is called the least upper bound of B if there is no upper bound z of B such that
zRx.
A lower bound x of B is called the greatest lower bound of B if there is no lower bound z of B such
that xRz.
Note that these bounds do not necessarily exist. Even if they exist, they are not necessarily in B. There
may be more than one upper or lower bound of B. However, if ...
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