## Relations

**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

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