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Verbal Description | All negative integers greater than $-5.$ |
---|---|

Roster Notation | ${-1,-2,-3,-4}$ |

Set-Builder Notation | ${x∣xis a negative integer greater than-5}$ |

Each way of describing a set will be discussed and a corresponding example will be shown.

the set of delicious dishesis not a valid description because

the set of desserts with chocolateis valid because including chocolate is an objective description.

$Example Set I:Example Set II:Example Set III: Desserts with chocolateCapital cities of the worldEuropean countries $

$Verbal Description:Roster Notation: Factors of9{1,3,9} $

Furthermore, the elements of a set are only considered once and their original order can be disregarded. In the example below, a set is created with the numbers of a given list.
$List:3,3,1,2↓Set:{1,2,3} $

Although the number $3$ occurs twice in the list, it is written only once in the set . $∣$or

$:$is written. Then, the common characteristics of the elements are defined. Finally, the whole notation is enclosed in curly brackets.

${-3,-1,1,3,5,…}↓{x∣xis an odd integer greater than-3} $

The symbols $∣$and

$:$are read as

such that.The above example can be read as

the set of all numbers $x$ such that $x$ is an odd integer greater than negative $3.$