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| The concept of equivalence is formalized as a relation ''R'' satisfying: | The concept of '''equivalence''' is formalized as a relation ''R'' satisfying: |
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| * ''a'', ''b'', and ''c'' are in an '''equivalence class'''. |
Relations
Relations are ordered pairs between sets.
Contents
Description
A relation takes members of two sets, A and B, and constructs ordered pairs.
A relation R between A and B is a subset of their Cartesian product. R ⊆ A × B.
A particular ordered pair (a,b) satisfying a relation R may be written as aRb.
The concept of equivalence is formalized as a relation R satisfying:
reflexivity: aRa
symmetry: aRb -> bRa
transitivity: aRb and bRc -> aRc
a, b, and c are in an equivalence class.