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- https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/Discrete_Structures/07%3A_Equivalence_Relations/7.02%3A_Equivalence_RelationsAn equivalence relation on a set is a relation with a certain combination of properties that allow us to sort the elements of the set into certain classes. Let A be a nonempty set. A relation ∼ on...An equivalence relation on a set is a relation with a certain combination of properties that allow us to sort the elements of the set into certain classes. Let A be a nonempty set. A relation ∼ on the set A is an equivalence relation provided that ∼ is reflexive, symmetric, and transitive. For a,b∈A , if ∼ is an equivalence relation on A and a ∼ b , we say that a is equivalent to b. In this section, we will focus on the properties that define an equivalence relation.
- https://math.libretexts.org/Bookshelves/Abstract_and_Geometric_Algebra/Rings_with_Inquiry_(Janssen_and_Lindsey)/01%3A_The_Integers/1.04%3A_The_Integers_modulo__mThe foundation for our exploration of abstract algebra is nearly complete. We need the basics of one more "number system" in order to appreciate the abstract approach developed in subsequent chapters.
- https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Book%3A_Mathematical_Reasoning__Writing_and_Proof_(Sundstrom)/07%3A_Equivalence_Relations/7.02%3A_Equivalence_RelationsAn equivalence relation on a set is a relation with a certain combination of properties that allow us to sort the elements of the set into certain classes. Let A be a nonempty set. A relation ∼ on...An equivalence relation on a set is a relation with a certain combination of properties that allow us to sort the elements of the set into certain classes. Let A be a nonempty set. A relation ∼ on the set A is an equivalence relation provided that ∼ is reflexive, symmetric, and transitive. For a,b∈A , if ∼ is an equivalence relation on A and a ∼ b , we say that a is equivalent to b. In this section, we will focus on the properties that define an equivalence relation.
