Chapter 1 · Mathematics
Roster Form and Set-builder Form
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Two ways to write one set: Roster form lists the elements, Set-builder form states their common property. When to use each.
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Key points
- Roster form: list all elements in curly brackets, separated by commas: {a, e, i, o, u}.
- In roster form order does not matter and elements are not repeated: SCHOOL gives {S, C, H, O, L}.
- Set-builder form: state the common property: {x : x is an even natural number, x ≤ 100}.
- The colon means such that.
- Use roster for small sets, set-builder for big or infinite sets.
Which form when?
| Form | Best for | Example |
|---|---|---|
| Roster | Small sets | {a, e, i, o, u} |
| Set-builder | Big or infinite sets | {x : x is a natural number} |
Try it yourself
Goal: Pick a rule and see the same set in roster and set-builder form, then test the order and no-repeat rules.
- Choose a property: even, odd, prime, multiple or perfect square.
- Move the slider to change the upper limit and watch the roster grow.
- Press No upper limit to see why infinite sets need set-builder form.
- Press Shuffle to check that order does not matter.
- Type any word and see which letters stay in the set.
Quick quiz
3 questions. Choose an answer for each, then submit to see your score and the explanations.
