SetBuilder 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 

{x^{2}  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
