A set is a collection of well-defined unique objects called elements. Sets are often illustrated by a Venn diagram, but there are several other ways to visualize them.

Verbal Description	All negative integers greater than $\text{-}5.$
Roster Notation	$\{\text{-}1,\text{-}2,\text{-}3,\text{-}4\}$
Set-Builder Notation	$\{x|x\text{ is a negative integer greater than }\text{-}5\}$

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

Verbal Description

A set can be described in words as long as there is no ambiguity of whether any particular object belongs to the set. For example, the set of delicious dishes is not a valid description because delicious is not well-defined. However, the set of desserts with chocolate is valid because including chocolate is an objective description.

Listing Method or Roster Notation

In listing method or roster notation, the elements of a set can be shown within curly brackets and separated by commas. The order of the elements is not relevant. 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. Although the number $3$ occurs twice in the list, it is written only once in the set .

Set-Builder Notation

In set-builder notation, sets are described by stating the common characteristics of its elements. To do this, a variable followed by $|$ or $:$ is written. Then, the common characteristics of the elements are defined. Finally, the whole notation is enclosed in curly brackets. 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 $3.$