= Relations =

'''Relations''' are ordered pairs between sets.

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== 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 [[Analysis/Sets#Operations|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'''.



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CategoryRicottone