A set of numbers shown in roster form lists all elements belonging to the set. In set-builder notation, however, all of the elements in a set can be described using a logical statement.
Roster Form
This form requires us to list all the natural numbers that are less than 11. We start with 1 and count all of them until 10, the largest natural number less than 11.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
We can now write the roster form of set P.
P={1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }
Set-Builder Notation
Often, it is more compact and easier to understand a set of numbers if they are listed in set-builder notation instead. We will use the variable p and a logical statement to describe the elements of set P.
P={p|p is a natural number, p < 11 }
