section_path: Definition and notation/Set-builder notation
section_name: Set-builder notation
paragraph_text: Set-builder notation
  
  Set-builder notation specifies a set as a selection from a larger set, determined by a condition on the elements. For example, a set F can be defined as follows:
  
  F = { n ∣ n is an integer, and 0 ≤ n ≤ 19 }. {\displaystyle F=\{n\mid n{\text{ is an integer, and }}0\leq n\leq 19\}.}
  
  In this notation, the vertical bar "|" means "such that", and the description can be interpreted as " F is the set of all numbers n such that n is an integer in the range from 0 to 19 inclusive". Some authors use a colon ":" instead of the vertical bar.