Set Builder Calculator
Generate set builder notation and roster form for mathematical sets with custom conditions
Define Your Set
Interval Notation
Includes 1, includes 10
Set Builder Notation
Reads as: "The set of all x such that 1 ≤ x ≤ 10, x ∈ ℤ}"
Roster Form
Contains 10 elements
Example: Odd Numbers Between 10 and 23
Problem Setup
Interval: (10, 23) - excludes endpoints
Number Type: Integers (ℤ)
Condition: Odd numbers only
Set Builder Notation
{x | 10 < x < 23, x ∈ ℤ, x is odd}
Roster Form
{11, 13, 15, 17, 19, 21}
Set Theory Symbols
Interval Types
[a, b] - Closed
Includes both endpoints
(a, b) - Open
Excludes both endpoints
[a, b) or (a, b]
Half-open intervals
Understanding Set Builder Notation
What is Set Builder Notation?
Set builder notation is a mathematical method for describing sets by specifying the properties that their members must satisfy. It's written in the form {x | condition}, which reads as "the set of all x such that the condition is true."
Components
- •Variable: Usually x, represents elements in the set
- •Vertical bar (|): Means "such that"
- •Condition: Mathematical property that x must satisfy
- •Domain: The set from which x is chosen (ℕ, ℤ, ℝ, etc.)
Roster vs Set Builder Form
Roster Form
Explicitly lists all elements:
{2, 4, 6, 8, 10}
Set Builder Form
Describes the pattern:
{x | 2 ≤ x ≤ 10, x ∈ ℤ, x is even}
Tip: Set builder notation is preferred for large or infinite sets, while roster form works well for small finite sets.