"동치관계"의 두 판 사이의 차이

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* ID :  [https://www.wikidata.org/wiki/Q130998 Q130998]

2020년 12월 26일 (토) 06:06 판

노트

  • As the name and notation suggest, an equivalence relation is intended to define a type of equivalence among the elements of \(S\).[1]
  • Every function \(f\) defines an equivalence relation on its domain, known as the equivalence relation associated with \(f\) .[1]
  • then the equivalence relation associated with \(f\) is the trivial relation, and hence \(S\) is the only equivalence class.[1]
  • The equivalence relation on \(S\) constructed in (10) is the equivalence relation associated with \(f\), as in (6).[1]
  • Show that R is an Equivalence Relation.[2]
  • Hence, Reflexive or Symmetric are Equivalence Relation but transitive may or may not be an equivalence relation.[2]
  • So let's begin with a digraph explanation of an equivalence relation.[3]
  • Some examples of equivalence relations to see why they're so basic is that the most fundamental one is equality.[3]
  • Finally, whenever you have a partition of a set, you can define an equivalence relation.[3]
  • And that is the story and multiple ways of understanding what equivalence relations are.[3]
  • A relation that is reflexive, symmetric, and transitive is called an equivalence relation .[4]
  • The last one enables me to point out how omnipresent equivalence relations actually are.[5]
  • An equivalence relation is a relation which "looks like" ordinary equality of numbers, but which may hold between other kinds of objects.[6]
  • Show that the less-than relation on the set of real numbers is not an equivalence relation.[6]
  • Check each axiom for an equivalence relation.[6]
  • Equivalence relations give rise to partitions.[6]
  • equivalence relation Let \(A\) be a nonempty set.[7]
  • For an equivalence relation, due to transitivity and symmetry, all the elements related to a fixed element must be related to each other.[8]
  • An equivalence relation allows us to regard two equivalent objects as being the same for some particular purpose.[9]
  • An ordering relation represents an equivalence relation if it is reflexive, symmetric, and transitive.[9]
  • We have an equivalence relation on strings: \(x \sim y\) if we can rearrange the O's of \(x\) to form \(y\).[10]
  • Members of a set are said to be in the same equivalence class if they have an equivalence relation.[11]
  • Each equivalence relation provides a partition of the underlying set into disjoint equivalence classes.[12]
  • A binary relation ~ on a set X is said to be an equivalence relation, if and only if it is reflexive, symmetric and transitive.[12]
  • Note that the equivalence relation generated in this manner can be trivial.[12]
  • (binary relations viewed as a subset of × ) is also an equivalence relation.[12]
  • The equivalence relation is a key mathematical concept that generalizes the notion of equality.[13]
  • Any relation that can be defined using expressions like “have the same” or “are the same” is an equivalence relation.[13]
  • Example 3 Determine whether the relation \(R\) given by the digraph is an equivalence relation.[13]
  • Determine whether the relation \(R\) given by the digraph is an equivalence relation.[13]
  • A setoid is a set equipped with an equivalence relation.[14]
  • Then the equivalence relation on S S is a way of making S S into the set of objects of such a groupoid.[14]
  • It may well be useful to consider several possible equivalence relations on a given set.[14]
  • For the history of the notion of equivalence relation see this MO discussion.[14]
  • Can we say the empty relation is an equivalence relation?[15]
  • We can say that the empty relation on the empty set is considered as an equivalence relation.[15]
  • But, the empty relation on the non-empty set is not considered as an equivalence relation.[15]
  • An equivalence relation on a set is a subset of , i.e., a collection of ordered pairs of elements of , satisfying certain properties.[16]

소스

  1. ↑ 1.0 1.1 1.2 1.3 Equivalence Relations
  2. ↑ 2.0 2.1 Equivalence Relations
  3. ↑ 3.0 3.1 3.2 3.3 Electrical Engineering and Computer Science
  4. ↑ equivalence relation
  5. ↑ Equivalence Relationship
  6. ↑ 6.0 6.1 6.2 6.3 Equivalence Relations
  7. ↑ 7.2: Equivalence Relations
  8. ↑ 6.3: Equivalence Relations and Partitions
  9. ↑ 9.0 9.1 Equivalence Relation - an overview
  10. ↑ Equivalence relations (CS 2800, Fall 2017)
  11. ↑ Equivalence relation | mathematics and logic
  12. ↑ 12.0 12.1 12.2 12.3 Equivalence relation
  13. ↑ 13.0 13.1 13.2 13.3 Equivalence Relations
  14. ↑ 14.0 14.1 14.2 14.3 equivalence relation in nLab
  15. ↑ 15.0 15.1 15.2 Definition, Proof and Examples
  16. ↑ Equivalence Relation -- from Wolfram MathWorld

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