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Describing Sets
List the elements, or describe the rule that decides what belongs — finite, infinite, and empty sets.
Two Ways to Describe a Set
A set can be described two ways:
- Listing: writing every element inside the brackets, such as {, , , }.
- Set-builder notation: describing the rule that elements must follow, such as { : is an even number, ≤ ≤ }.
Set-builder notation is read as "the set of all , such that is an even number, and is between and ".
Example 1 — listing to set-builder
Write {, , , , } using set-builder notation.
- Describe what these numbers have in common: they are whole numbers from to .
- Write the rule: { : is a whole number, ≤ ≤ }
Answer: { : is a whole number, ≤ ≤ }
Example 2 — set-builder to listing
List the set { : is a factor of }.
- Find every whole number that divides evenly into : , , , , , .
- Write the set: {, , , , , }
Answer: {, , , , , }
Finite, Infinite, and Empty Sets
| Types of sets by size | ||
|---|---|---|
Practice
Which of these describes an infinite set?
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