# Write sets using set notation

Write sets using set notation

A set is a collection of objects called the elements or members of the set. In algebra, the elements of a set are usually numbers. Set braces, { }, are used to enclose the elements.

For example, 2 is an element of the set {1, 2, 3}. Since we can count the number of elements in the set {1, 2, 3}, it is a finite set.

In our study of algebra, we refer to certain sets of numbers by name. The set

N 5 {1, 2, 3, 4, 5, 6, . . . } is called the

natural numbers or the counting numbers. The three dots

show that the list continues in the same pattern indefinitely. We cannot list

all of the elements of the set of natural numbers, so it is an infinite set.

When 0 is included with the set of natural numbers, we have the set of

whole numbers, written W 5 {0, 1, 2, 3, 4, 5, 6, . . . }.

A set containing no elements, such as the set of whole numbers less than 0,

is called the empty set, or null set, usually written .

Caution

Do not write {ø } for the empty set; { ø } is a set with one element, . Use

only the notation for the empty set.

In algebra, letters called variables are often used to represent numbers

or to define sets of numbers. For example,

{x | x is a natural number between 3 and 15}

(read “the set of all elements x such that x is a natural number between 3 and

15”) defines the set

{4, 5, 6, 7, . . . , 14}.

The notation {x | x is a natural number between 3 and 15} is an example

of set-builder notation.

{ x | x has property P }

the set of all elements x such that x has a given property P