04d real numbers, sets, and interval notation · closed intervals are indicated by closed circles...
TRANSCRIPT
R (Real)
I (Irrational)N (Natural)
Q (Rational)
W (Whole)
Z (Integers)
04d Real Numbers, Sets, and Interval Notation
Sets Set = a collection of objects
the objects are elements of the set
If B is a set, the notation a ∈ B means that a is an element in the set B and the notation c ∉ B means that c is not an element in the set B.
Some sets can be listed with braces : for instance A = {1,2,3,4} (the set A has 4 elements which are 1,2,3,4)
Some sets can be written using set builder notation: D = { x | x > 10} which is read D is the set of all x's such that x is greater than 10
Set Union, Intersection, or Empty: Union: Given H and G then H ∪ G means the set that contains the elements of H and G
Intersection: H ∩ G means the set that contains just the elements H & G have in common
Empty: ∅ means there are no elements in the set
EX: Given H = {1,2,3,4,5} G = {4,5,6,7,8} M = {9,10,11}
H ∩ G = H∪ G = M ∩ G =
H ∪ M = M ∪ G = H ∩ M =
H∩G∩M = H∪G∩M =
Ex5:__________________ 25:_________________
1/7:_________________ 3π:_________________
Objective: Identify and classify real numbers, sets of numbers, and represent numbers using interval notation
Intervals Interval Notation
Interval Notation Set Description Graph
(a, b)
{x∈R|a < x < b}
a b
(a, b]
{x∈R| x > a} a
(∞, b)
b
(∞, +∞)
Open Intervals are indicated by open circles on a number line and by ( ) in interval notation these mean that the number isn't included in the answer.
Closed Intervals are indicated by closed circles on a number line and by [ ] in interval notation these mean that the number is included in the answer.
EX: Use the above chart to fill in the missing pieces
(5, 12]
{x∈R| 3 < x < 15}
[9, ∞)
20
{x∈R| x > 123}
(4, 3) U (5, 20]
2 3 8
{x∈R|8 < x < 15} U {x∈R|x > 25}
Interval Set Builder Graph