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The elements of a set may differ in many ways. Sometimes we want to single out some of their properties or attributes. An equivalence relation allows one to relate and “identify” elements that have the same properties. For instance, the relation “has the same model year” is an equivalence relation on the set of cars. In this chapter, we derive the most common properties of equivalence relations and give some applications.

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Equivalence Relations

  • 章节

  • 发表日期：

    2025年

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  • Andreas Klappenecker,
  • Hyunyoung Lee

摘要

The elements of a set may differ in many ways. Sometimes we want to single out some of their properties or attributes. An equivalence relation allows one to relate and “identify” elements that have the same properties. For instance, the relation “has the same model year” is an equivalence relation on the set of cars. In this chapter, we derive the most common properties of equivalence relations and give some applications.