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Relations describe the relationships between different elements of the same set or different sets. They are another fundamental concept in mathematics, for instance, they provide a foundation of functions, which turn out to be special cases of relations.

We will see in this part of BookofProofs that, from the set-theoretical point of view, relations are sets. As such, being the set element $”\in”$ or being the subset $”\subseteq”$ are not relations, but predicates. Loosely speaking, they are relations in a metalanguage, which deals with sets.

Apart from these “metarelations”, there are many examples of “usual” relations we deal with in mathematics, for instance order relations $”\ge”$, the perpendicularity $”\perp”$ of straight lines in a plane, the equivalence relations and many, many more.

| | | | created: 2014-02-20 21:16:45 | modified: 2018-12-09 23:41:35 | by: bookofproofs

1.Definition: Ordered Pair, n-Tuple

2.Motivation: Usage of Ordered Tuples In Other Mathematical Disciplines

3.Definition: Cartesian Product

4.Definition: Relation

5.Binary Relations and Their Properties

6.Definition: Equivalence Relation

7.Functions (Maps)

8.Order Relations

Edit or AddNotationAxiomatic Method

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Bibliography (further reading)