# The cardinality of a relation is

## Introduction

In mathematics, the cardinality of a set means the number of its elements, and this concept can be extended to any finite mathematical structure. In the case of a binary relation, cardinality is simply the number of ordered pairs that make up the relation.

### What is the cardinality of a relation?

In mathematics, the cardinality of a set is a measure of the “number of elements” of the set. For example, the set A = {1, 2, 3} has cardinality 3. There are two approaches to cardinality – one which compares sets directly using bijections and injections, and another which uses cardinal numbers.

The most common definition of cardinality is probably the one which uses cardinal numbers. In this approach, two sets have the same cardinality if there exists a bijection between them. In other words, two sets have the same cardinality if they can be put into one-to-one correspondence.

### Why is the cardinality of a relation important?

Cardinality is important because it helps to determine the number of possible relationships that can exist between two sets of data. For example, if you have a set of data containing information about all the people in your neighborhood, the cardinality of the relation between the set of people and the set of neighborhoods they live in would be one-to-many. This means that for each person in the neighborhood, there is only one neighborhood they can live in (the cardinality of the neighborhood set is one), but each person can live in multiple neighborhoods (the cardinality of the people set is many).

## The Three Types of Cardinality

In mathematics, the cardinality of a set is a measure of the “size” of the set. Informally, it is the number of elements in the set. The cardinality of a set is denoted using cardinality notation, such as 3 or ∞. In this article, we’ll discuss the three types of cardinality: finite, countably infinite, and uncountably infinite.

### One-to-One (1:1)

In database terms, cardinality refers to the number of relationships between data points. The three types of cardinality are one-to-one (1:1), one-to-many (1:N), and many-to-many (M:N). Each type of cardinality has certain characteristics that make it unique.

One-to-one (1:1) relationships are the most straightforward. As the name suggests, in a 1:1 relationship, each data point is related to only one other data point. For example, a social security number can be related to only one person. In a database, 1:1 relationships are often used to store information that is too sensitive to be stored in the main database table.

One-to-many (1:N) relationships are more complex than 1:1 relationships. In a 1:N relationship, each data point in the first table can be related to multiple data points in the second table. For example, a single customer can have multiple orders. In a database, 1:N relationships are used to store information about hierarchical data structures.

Many-to-many (M:N) relationships are the most complex type of cardinality. In an M:N relationship, each data point in the first table can be related to multiple data points in the second table and vice versa. For example, a single order can be related to multiple customers and a single customer can placed multiple orders. In a database, M:N relationships are used to store information about cross-referenced data.

### One-to-Many (1:N)

The term cardinality means the number of a given element within a set. In the relational database world, cardinality refers to the number of occurrences of one entity for each occurrence of another entity. Three specific terms are used to describe the cardinality of a relationship: one-to-one (1:1), one-to-many (1:N), and many-to-many (M:N).

In a one-to-one relationship, an instance in entity A corresponds to one, and only one, instance in entity B. A real life example might be a social security number corresponding to only one employee. The two entities must share a common attribute or set of attributes so that they can be linked together. If two people in the United States happen to have the same social security number, then our 1:1 relationship has failed. In this case, we would need to add another attribute or set or attributes to distinguish between these two people.

A one-to-many relationship exists when for one instance of an entity there can be multiple related instances in another entity. For example, each customer might have multiple orders. The customer is on the “one” side of the relationship and orders are on the “many” side. In this type of relationship, the foreign key is located on the many side of the relationship.

### Many-to-Many (M:N)

Many-to-many (M:N) is a relationship where a single row in table A can relate to multiple rows in table B, and vice versa. A many-to-many relationship requires a third table, called a junction table, to break up the relationship in to two one-to-many relationships. In the data model diagram below, notice how the junction table sales has foreign keys to both the products and customers tables. This relationship is read as “Many sales can be made for each product, and many sales can be made for each customer.”

One-to-Many (1:M)
In a one-to-many relationship, a row in table A can relate to multiple rows in table B, but a row in table B can only relate to one row in table A. You can think of this as one parent, many children. In the example below, each customer has made multiple purchases, but each purchase was made by only one customer.

Many-to-One (M:1)
A many-to-one relationship is the inverse of a one-to-many relationship. In this type of relationship, a row in table A can relate to only one row in table B, but a row in information_schema InnoDB MySQL Oracle PostgreSQL SQL Server SQLite3
Many databases have an information_schema database which contains meta data about all the other databases on that server. The meta data includes information about tables and columns, as well as views, stored procedures and functions. The information_schema database is read only; you cannot write data to it.

## How to Determine the Cardinality of a Relation

The cardinality of a relation is the number of tuples in the relation. The cardinality of a relation R is denoted by |R|. To determine the cardinality of a relation, you need to determine the number of tuples in the relation.

### Look at the Number of Rows

To find the cardinality of a relation, simply look at the number of rows in the table. The cardinality of a relation is always equal to the number of rows in the table. So, if there are five rows in the table, then the cardinality of the relation is five.

### Look at the Number of Columns

To determine the cardinality of a relation, look at the number of columns in the relation. The cardinality of a relation is the number of columns in the relation.

For example, consider the following relation:

``customer(customer_id, name, address, phone)``

This relation has four columns, so the cardinality of this relation is four.

## Examples of Cardinality

In mathematics, the cardinality of a set is a measure of the “number of elements” of the set. For example, the set A = {1, 2, 3} has a cardinality of 3. We can also say that the cardinality of A is 3.

### One-to-One (1:1)

In a one-to-one relationship, each record in Table A can have only one record in Table B, and vice versa. For example, each employee can have only one job title, and each job title can be given to only one employee.

### One-to-Many (1:N)

Cardinality is the term describing the relationship between different sets of data. In databases, cardinality refers to the number of columns in a table that are related to another column in another table. The cardinality of a relation is the number of tuples (rows) in one table that are associated with a tuple in another table.

For example, consider a customer database containing two tables: Customers and Orders. The Customers table has a column for customer ID, and the Orders table has a column for customer ID. The Customers table also has other columns such as name and address, while the Orders table has other columns such as product ID and quantity.

The cardinality between these two tables would be one-to-many (1:N), because for each customer in the Customers table, there can be multiple orders in the Orders table. In other words, each row in the Customers table is related to zero, one, or many rows in the Orders table.

### Many-to-Many (M:N)

A many-to-many relationship occurs when each record in Table A may be linked to multiple records in Table B, and vice versa. In this example, we have a situation where Customers can make many Purchases, but each Purchase can be made by more than one Customer.

## Conclusion

In mathematics, the cardinality of a set is a measure of the “number of elements” of the set. For example, the set A = {1, 2, 3} has a cardinality of 3. There are two approaches to cardinality – one which compares sets directly using bijections and injections, and another which uses cardinal numbers.