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
|