Set-builder notation

Definition

Set-builder notation is a mathematical notation used to define a set by specifying a property that its members must satisfy. It typically takes the form $\{ x \mid \text{condition on } x \}$.

5 Must Know Facts For Your Next Test

1. Set-builder notation often uses a vertical bar or colon to mean 'such that' (e.g., $\{ x \mid x > 0 \}$).
2. It can define sets with both simple and complex conditions, including inequalities and multiple criteria.
3. The variable in set-builder notation represents elements of the set being defined.
4. Set-builder notation is particularly useful for defining domains and ranges of functions.
5. It is commonly used in contexts involving linear inequalities and absolute value inequalities.

Review Questions

• What does the vertical bar in set-builder notation signify?
• How would you write the set of all real numbers greater than 5 using set-builder notation?
• Explain how set-builder notation can be used to define the domain of a function.

Related terms

Inequality: A mathematical statement that shows the relationship between two expressions that are not equal, using symbols like $>$, $<$, $\geq$, or $\leq$.

Domain: The set of all possible input values for which a function is defined.

Range: The set of all possible output values produced by a function.