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

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.