# Collection - Set

A set is:

The objects element of the set have the same type (the type may be a composed type such as a tuple)

The mathematical concept of a set is a group of unique items, meaning that the group contains no duplicates (theory) but many data application have extended this definition with a bag (multiset) (such as a table)

The set is used to perform distinct operation (ie deleting duplicates)

## Examples

### In Programming language

Some real-world examples of sets include the following:

• The set of uppercase letters 'A' through 'Z'
• The set of nonnegative integers {0, 1, 2 …}
• The set of reserved Java programming language keywords {'import', 'class', 'public', 'protected'…}
• A set of people (friends, employees, clients, …)
• The set of records returned by a database query - See resulset (in java)
• The set of Component objects in a Container
• The set of all pairs
• The empty set {}

### In Computer Science

• The idea of a “connection pool” is a set of open connections to a database server.
• Web servers have to manage sets of clients and connections.
• File descriptors provide another example of a set in the operating system.

## Basic properties of sets

The basic properties of sets:

• Sets contains only one instance of each item
• Sets may be finite or infinite
• Sets can define abstract concepts

## Set expression

### Set of Non-negative number

In Mathese, “the set of non-negative numbers” is written like this:

where:

• The colon stands for “such that”
• the part before the colon specifies the elements of the set, and introduces a variable to be used in the second part
• the part after the colon: defines a filter rule

The above notation can also be shortened if x is wel known :

### Another example

Another example where the set consists of and

### Tuple

Tuples examples in set expression:

• The set expression of all pairs of real numbers in which the second element of the pair is

the square of the first can be written:

of abbreviated:

• The set expression of triples consisting of nonnegative real numbers.