Relational Mathematics: Encyclopedia of Mathematics and Its Applications 132

Relational mathematics is a branch of mathematics that studies relations, which are mathematical objects that represent relationships between sets. Relations are used to model a wide variety of phenomena in mathematics, computer science, and other fields. The Encyclopedia of Mathematics and Its Applications, Volume 132, provides a comprehensive overview of relational mathematics, covering topics such as:

* The foundations of relational mathematics * The different types of relations * The properties of relations * The operations that can be performed on relations * The applications of relations

Relational Mathematics (Encyclopedia of Mathematics and its Applications Book 132)

by Gunther Schmidt

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Language	:	English
File size	:	15090 KB
Print length	:	582 pages

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The Foundations of Relational Mathematics

The foundations of relational mathematics are based on the concept of a set. A set is a collection of distinct objects. The objects in a set are called elements. Relations are then defined as subsets of the Cartesian product of two sets. The Cartesian product of two sets A and B is the set of all ordered pairs (a, b) where a is an element of A and b is an element of B.

The Different Types of Relations

There are many different types of relations. The most common types of relations are:

* Equivalence relations: An equivalence relation is a relation that is reflexive, symmetric, and transitive. * Order relations: An order relation is a relation that is reflexive, transitive, and antisymmetric. * Partial order relations: A partial order relation is a relation that is reflexive, transitive, and anti-reflexive.

The Properties of Relations

Relations have a number of properties that can be used to classify them. The most important properties of relations are:

* Reflexivity: A relation is reflexive if every element of the set is related to itself. * Symmetry: A relation is symmetric if whenever a is related to b, then b is related to a. * Transitivity: A relation is transitive if whenever a is related to b and b is related to c, then a is related to c. * Anti-reflexivity: A relation is anti-reflexive if no element of the set is related to itself. * Asymmetry: A relation is asymmetric if whenever a is related to b, then b is not related to a.

The Operations that Can Be Performed on Relations

There are a number of operations that can be performed on relations. The most common operations are:

* Union: The union of two relations is the set of all elements that are related to either relation. * Intersection: The intersection of two relations is the set of all elements that are related to both relations. * Complement: The complement of a relation is the set of all elements that are not related to the relation. * Inverse: The inverse of a relation is the relation that is obtained by reversing the order of the elements in each ordered pair.

The Applications of Relations

Relations have a wide variety of applications in mathematics, computer science, and other fields. Some of the most common applications of relations include:

* Modeling relationships between objects * Representing data in databases * Defining orderings on sets * Solving problems in graph theory * Developing algorithms for computer science

Relational mathematics is a powerful tool that can be used to model a wide variety of phenomena. The Encyclopedia of Mathematics and Its Applications, Volume 132, provides a comprehensive overview of relational mathematics, making it an essential resource for anyone who wants to learn more about this important topic.

Relational Mathematics (Encyclopedia of Mathematics and its Applications Book 132)

by Gunther Schmidt

5 out of 5

Language	:	English
File size	:	15090 KB
Print length	:	582 pages

FREE