Set-builder notation describes a set by a rule (“all even integers between 1 and 20”), while roster notation lists its members. Moving between them is a key skill for algebra, probability and computer science.
How to use the Set Builder Calculator
- Left endpoint
- Right endpoint
- Endpoints
- Type of numbers
- Condition
- Spacing
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Choose the endpoints, whether they are included, the kind of numbers and an optional condition. The calculator lists the members (up to 200) and writes the rule.
Formula
{x | a ≤ x ≤ b, x ∈ ℤ, condition} ↔ {listed members}
Worked example
Inputs — Left endpoint: 1; Right endpoint: 20; Endpoints: Both inclusive; Type of numbers: Integers ℤ; Condition: Prime numbers.
Results — Set-builder notation = {x | 1 ≤ x ≤ 20, x ∈ ℤ, x is prime}; Roster notation = {2, 3, 5, 7, 11, 13, 17, 19}; Number of members = 8.
Key terms
- Set-builder notation
- {x | rule}, the set of x satisfying a rule.
Frequently asked questions
What does {x
x > 3} mean? | The set of all x such that x is greater than 3.
What is roster notation?
Listing the members, e.g. {2, 3, 5, 7}.
Why can't real intervals be listed?
They contain uncountably many numbers.
Does ℕ include 0?
Conventions differ; this calculator treats ℕ as the non-negative integers in the range.