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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/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/04%3A_Relations
- https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Book%3A_Mathematical_Reasoning__Writing_and_Proof_(Sundstrom)/07%3A_Equivalence_RelationsThe notion of a function can be thought of as one way of relating the elements of one set with those of another set (or the same set). A function is a special type of relation in the sense that each e...The notion of a function can be thought of as one way of relating the elements of one set with those of another set (or the same set). A function is a special type of relation in the sense that each element of the first set, the domain, is “related” to exactly one element of the second set, the codomain. This idea of relating the elements of one set to those of another set using ordered pairs is not restricted to functions.
- https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/Discrete_Structures/07%3A_Equivalence_RelationsThe notion of a function can be thought of as one way of relating the elements of one set with those of another set (or the same set). A function is a special type of relation in the sense that each e...The notion of a function can be thought of as one way of relating the elements of one set with those of another set (or the same set). A function is a special type of relation in the sense that each element of the first set, the domain, is “related” to exactly one element of the second set, the codomain. This idea of relating the elements of one set to those of another set using ordered pairs is not restricted to functions.
- 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.
