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    Equivalence Relation and Equivalence Sets

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    Topology
    Sets and Functions (XLVI)
    Functions

    In the set R of all real numbers, let x ~ y means that x - y is an integer.
    Show that this is an equivalence relation and describe the equivalence sets.

    See the attached file.

    © BrainMass Inc. brainmass.com December 24, 2021, 6:53 pm ad1c9bdddf
    https://brainmass.com/math/geometry-and-topology/equivalence-relation-and-equivalence-sets-147741

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    Solution Summary

    This solution is comprised of a detailed explanation of the properties of the equivalence relation. It contains step-by-step explanation of the following problem: In the set R of all real numbers, let x ~ y means that x - y is an integer. It shows that this is an equivalence relation and describe the equivalence sets.

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