For example, if \[ U \]is the set whose members are the numbers 1, 2, and 3, then:

\[ U = \{1, 2, 3\}. \]

Note that the order of the elements in the braces does not matter. Therefore:

\[ \{ 2, 1, 3 \} = \{3, 2, 1 \} = \{ 1, 2, 3 \} = U. \]

Any set with a finite number of members is a **Finite** set.

Any set whose members can be put in a one-to-one relationship with the set of natural numbers is called a **Countably Infinite** set.

A set that is either finite or countably infinite is called **Countable**.

An infinite set that cannot be put into a one-to-one relationship with the set of natural numbers is called an **Uncountable** set.

The set of natural numbers, the set of integers, and the set of rational numbers are examples of countable sets.

The set of irrational numbers and the set of real numbers are examples of uncountable sets.