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Set-Builder Notation

A shorthand used to write sets, often sets with an infinite number of elements.

Note: The set {x : x > 0} is read aloud, "the set of all x such that x is greater than 0." It is read aloud exactly the same way when the colon : is replaced by the vertical line | as in {x | x > 0}.

General Form: {formula for elements: restrictions} or
{formula for elements| restrictions}

Examples: {x: x ≠ 3} the set of all real numbers except 3
  {x | x < 5} the set of all real numbers less than 5
  {x2 | x is a real number} the set of all real numbers greater than or equal to 0
  {2n + 1: n is an integer} the set of all odd integers (e.g. ..., -3, -1, 1, 3, 5,...).

 

See also

Interval notation, real numbers, integers, cardinality

 


  this page updated 27-aug-12
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons
NCTM Web Bytes December 2004 Web Bytes March 2005 Web Bytes