Set builder notation

Definition

Set builder notation is a mathematical shorthand used to describe sets by stating the properties that its members must satisfy. It is typically written in the form {x | property of x}.

5 Must Know Facts For Your Next Test

1. Set builder notation uses curly braces {} and a vertical bar | to separate elements and their defining properties.
2. The expression {x | x > 0} describes the set of all positive numbers.
3. Elements described in set builder notation can belong to any type of set, including finite, infinite, and intervals.
4. Set builder notation can also be used with more complex conditions such as {x ∈ ℝ | x^2 < 4}.
5. It is often used in conjunction with logical symbols like ∈ (element of), ∧ (and), and ∨ (or).

Review Questions

• What symbols are commonly used in set builder notation?
• How would you write the set of all integers greater than 10 using set builder notation?
• Can you use set builder notation to describe an interval? Provide an example.

Related terms

Element: An individual object contained within a set.

Interval Notation:

A way of writing subsets of the real number line using intervals.

Empty Set: A set that contains no elements, denoted by {} or ∅.