What is the point of a partial order? a. We would like to generalize the properties of the relation x=yx=y to objects that are "basically the same," if not necessarily equal. b. We would like to generalize the properties of the relation x

What is the point of a partial order? a. We would like to generalize the properties of the relation x=yx=y to objects that are "basically the same," if not necessarily equal. b. We would like to generalize the properties of the relation x

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 14E: In each of the following parts, a relation is defined on the set of all human beings. Determine...

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Question

What is the point of a partial order?

We would like to generalize the properties of the relation x=yx=y to objects that are "basically the same," if not necessarily equal.

We would like to generalize the properties of the relation x<yx<y to objects that do not naturally satisfy a total order in the way that numbers do.

We would like to generalize the properties of the relation x≤yx≤y to objects that do not naturally satisfy a total order in the way that numbers do.

There is no point. We make up mathematical objects for fun.

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