Two Ways to Represent Sets

There are two main ways to represent sets: roster notation and set-builder notation.

Roster notation lists all the elements of a set inside curly brackets {}. This method is useful when the number of elements is small and they can be clearly listed.
For example, the set of natural numbers from 1 to 5 can be written as:
$\{ 1, 2, 3, 4, 5 \}$

Set-builder notation does not list the elements directly. Instead, it uses a condition or property that the elements of the set must satisfy.
For example, the set of odd natural numbers between 1 and 100 can be written as:

$\{ x \in \mathbb{N} \mid 1 \le x \le 100 \land x\ \text{is odd} \}$

Depending on the situation, either method can be used. Set-builder notation is especially useful when the set has many elements or follows a specific rule, making the expression more concise and clear.