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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,...).