In the set of real numbers R, we may define the 'strict' inequality as relation Vx, y E R, xRy +x < y. Explain an example showing why this only a partial order on the set of real numbers.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...
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In the set of real numbers R, we may define the 'strict' inequality as relation Vx, y E R,
xRy + x < y. Explain an example showing why this only a partial order on the set of real
numbers.
Transcribed Image Text:In the set of real numbers R, we may define the 'strict' inequality as relation Vx, y E R, xRy + x < y. Explain an example showing why this only a partial order on the set of real numbers.
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