Definition 5.2.1.
The contents of a set can be described by listing the elements of the set, separated by commas, inside a set of curly brackets. This way of describing a set is called roster form.
Section 5.2 Roster Form
So far, we have described the elements of sets with words. Roster form is a shorter method that lists every element of a set. We can also use an ellipsis when the pattern in the list is clear.
In the video in Figure 5.2.2 we review the definition of roster form and give the first examples.
We give examples of sets in roster form along with a verbal description.
Example 5.2.3. Sets in roster form.
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\(\{1, 2, 3, 4\}\) is the set containing the numbers 1, 2, 3, and 4.
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\(\{\mathtt{w}, \mathtt{x}, \mathtt{y}, \mathtt{z}\}\) is the set containing the letters \(\mathtt{w}, \mathtt{x}, \mathtt{y}\text{,}\) and \(\mathtt{z}\text{.}\)
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\(\{ \text{red}, \text{yellow}, \text{blue} \}\) is the set containing red, yellow, and blue.
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\(\{5,3,\mathtt{w}\}\) is the set containing the numbers \(5\) and \(3\) and the letter \(\mathtt{w}\text{.}\)
Recall that an ellipsis (\(\ldots\)) shows that the pattern is continued. We can use an ellipsis when writing a set in roster form instead of listing every element.
Example 5.2.4. Sets in roster from with ellipsis.
We give examples of sets written in roster form that use ellipses.
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\(\{\mathtt{c},\mathtt{d},\mathtt{e},\ldots,\mathtt{n}\}\) is the set of letters from \(\mathtt{c}\) to \(\mathtt{n}\text{.}\)
Roster form also allows us to formulate a set that does not contain any elements by writing \(\{ \}\text{.}\)
Definition 5.2.5.
The empty set (also called the null set) is the set that consists of no elements. It is denoted by \(\{ \}\text{.}\)
The empty set contains no elements. In particular it does not contain the number \(0\text{.}\)
