**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*