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Roster Notation: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Roster NotationRoster Notation: Definition and ExamplesTable of ContentsRoster Notation in Math Definition of Roster Notation

Roster notation (also called roster form) is a way of representing a set by listing all its elements within curly brackets, separated by commas. In mathematics, a set is a collection of distinct, well-defined objects, and the roster form provides a straightforward visual representation of these elements. One important feature of roster notation is that the order of elements doesn't matter - only their membership in the set is significant.

While roster notation is simple and direct, it has limitations. When dealing with large sets, listing every element becomes impractical. To overcome this, mathematicians use ellipsis points (three dots "...") to indicate a continuing pattern. For infinite sets, the notation shows the pattern and ends with ellipsis points. Alternative names for roster notation include enumeration notation and tabular method, as it essentially enumerates or tabulates all elements of a set.

Examples of Roster Notation Example 1: Writing Odd Numbers Less Than 101010 in Roster Form Problem:

Write the set of odd numbers less than 101010 in a set notation form. What is the cardinality of the set?

Step-by-step solution:

Step 1, Let's identify all odd numbers less than 101010. Odd numbers are numbers that leave a remainder of 111 when divided by 222.

Step 2, List these odd numbers: 111, 333, 555, 777, 999.

Step 3, Write these numbers in roster notation with curly brackets: {1,3,5,7,9}\{1, 3, 5, 7, 9\}{1,3,5,7,9}

Step 4, Count the total number of elements to find the cardinality. There are 555 odd numbers less than 101010, so the cardinality of the set is 555.

Example 2: Expressing Sets P and Q in Roster Form Problem:

Express the sets PPP and QQQ in the roster form.

Expressing Sets P and Q in Roster Form

Step-by-step solution:

Step 1, Look at set PPP in the diagram and list all elements inside it.

Step 2, Set PPP contains the numbers 333, 555, 777, and 999. Write these in roster form as P={3,5,7,9}P = \{3, 5, 7, 9\}P={3,5,7,9}

Step 3, Now look at set QQQ in the diagram and list all elements inside it.

Step 4, Set QQQ contains the letters MMM, NNN, PPP, and QQQ. Write these in roster form as Q={M,N,P,Q}Q = \{M, N, P, Q\}Q={M,N,P,Q}

Example 3: Converting Set Builder Form to Roster Notation Problem:

Express the set P={p:p=2k+1,2k7}P = \{p : p = 2k + 1, 2 P={p:p=2k+1,2k7} in the roster notation.

Step-by-step solution:

Step 1, Understand what the set builder notation means. It says p equals 2k+12k + 12k+1, where kkk is greater than 222 but less than 777.

Step 2, Find all possible values of kkk within the given range. Since kkk must be greater than 222 and less than 777, kkk can be 333, 444, 555, or 666.

Step 3, Calculate ppp for each value of kkk using the formula p=2k+1p = 2k + 1p=2k+1:

When k=3k = 3k=3, ppp = 222 × 333 + 111 = 777 When k=4k = 4k=4, ppp = 222 × 444 + 111 = 999 When k=5k = 5k=5, ppp = 222 × 555 + 111 = 111111 When k=6k = 6k=6, ppp = 222 × 666 + 111 = 131313

Step 4, Write all calculated values of p in roster form: P={7,9,11,13}P = \{7, 9, 11, 13\}P={7,9,11,13}

Comments(1)AArtTutorJillNovember 6, 2025This glossary page on roster notation is great! I've used it to help my students grasp the concept. Clear defs and examples really aid learning.

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