Set-Builder Notation

Set Theory · Axiom Academy

Describe infinite and complex sets using properties instead of listing elements. Set-builder notation has the form: variable : condition . The colon (or vertical bar |) means "such that." We can describe all even numbers by specifying what makes a number even. Often we specify WHERE the variable comes from (its domain) before the condition. We can combine multiple conditions using logical operators (and, or). Here are some commonly used sets defined with set-builder notation.

This is the written version of the interactive lesson above. See the full Set Theory course.