--- aliases: [roster notation] --- #sets-functions ## Definition > [!tldr] Definition > **Roster notation** is a way of writing [[set]] in which the set [[Set|elements]] are given explicitly in a list, surrounded by curly braces. Notes: - If the set is finite, then the set in roster notation is just a list of all its elements. - If the set is infinite, correct roster notation would list enough elements to indicate the pattern for inclusion in the set, then indicate that the pattern continues with dots ($\dots$). If it's difficult or impossible to indicate a pattern, [[Set-builder notation|set-builder notation]] or an English description is usually more appropriate. - The [[Empty set|empty set]] $\emptyset$ is considered to be in roster notation -- there's nothing in it, so there's nothing to list. ## Examples and Non-Examples - The set of all positive integers less than 7, written in roster notation is $\{1,2,3,4,5,6\}$. - The set of all positive divisors of 20, written in roster notation is $\{1,2,4,5,10,20\}$. - The set of all positive *multiples* of 20, on the other hand, is infinite. In roster notation this would look like $\{20, 40, 60, 80, 100, \dots\}$ where the dots indicate that the pattern (which is supposed to be apparent from the items that are listed) continues. ## Resources <div style="padding:56.25% 0 0 0;position:relative;"><iframe src="https://player.vimeo.com/video/602744516?badge=0&amp;autopause=0&amp;player_id=0&amp;app_id=58479" frameborder="0" allow="autoplay; fullscreen; picture-in-picture" style="position:absolute;top:0;left:0;width:100%;height:100%;" title="Screencast 3.2: Roster and set-builder notation"></iframe></div> Other resources: - Tutorial: [Roster form](https://www.cuemath.com/algebra/roster-notation/) - Tutorial: [Roster notation](https://www.mathdoubts.com/roster-notation/)