R.4. Consider the relation R = {(f, g): f, g:R → R& f(2) < g(2)}. (The notation used here indicates that fand g are functions with domain the set of all real numbers and range a subset of the set of real numbers.) Show that R defines a preorder on the set of real functions, but it does not define a partial order on the set of real functions.
R.4. Consider the relation R = {(f, g): f, g:R → R& f(2) < g(2)}. (The notation used here indicates that fand g are functions with domain the set of all real numbers and range a subset of the set of real numbers.) Show that R defines a preorder on the set of real functions, but it does not define a partial order on the set of real functions.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 24E: For any relation on the nonempty set, the inverse of is the relation defined by if and only if ....
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