Transcript Set Builder Notation

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 sometimes written with a colon : instead
of a |
• { 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,...).
Interval Notation
• A notation for representing an interval
as a pair of numbers. The numbers are
the endpoints of the interval.
• Parentheses and/or brackets are used
to show whether the endpoints are
excluded or included. For example,[3, 8)
is the interval of real numbers between
3 and 8, including 3 and excluding 8.
Other Notation
-3≤x≤2 or
3≤x<8
Homework
Page 261