5. Working With Sets
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How does roster form differ from set-builder notation?
Roster Form:
G={ 1, 3, 5, 7, 9, 11, 13, 15, 17 }
Set-Builder Notation:
G={x|x is an odd natural number less than 18}
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.
The set only consists of odd numbers, so we can eliminate any even numbers from the set of all natural numbers. 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21... Finally, we know that the set only contains odd natural numbers that are less than18. We can now form the roster form of set G. G={ 1, 3, 5, 7, 9, 11, 13, 15, 17 }
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 x and a logical statement to describe the elements of set G. G = { x|x is an odd natural number less than18 }