# 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.

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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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