One of the theorems is called well-ordered theorm: .a For any set A ,we have |A|<|P(A)| .b If S is ordered-isomorphic to T, then |S|=|T| .c Every set can be well-ordered. .d Let X be anonempty partially ordered set in which every ordered subset has an upper bound in X. Then X contains at least one maximal element.
One of the theorems is called well-ordered theorm: .a For any set A ,we have |A|<|P(A)| .b If S is ordered-isomorphic to T, then |S|=|T| .c Every set can be well-ordered. .d Let X be anonempty partially ordered set in which every ordered subset has an upper bound in X. Then X contains at least one maximal element.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 13E: 13. Consider the set of all nonempty subsets of . Determine whether the given relation on is...
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