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P.1 Real Numbers
Algebra III
Real Number System
Natural
{1, 2, 3, 4,…}
How many
natural numbers
are there?
Real Number System
Natural
Whole
What is the difference
between natural and
whole?
How many whole
numbers are there?
{0, 1, 2, 3, 4,…}
Is every whole number
a natural number?
Real Number System
Natural
Whole
Integers
{...-3, -2, -1, 0, 1, 2, 3, …}
How many integers
are there?
Real Number System
Natural
Whole
Integers
Rational
Fractions
How many rational
numbers are
there?
a

 a, b  I , b  0
b

Real Number System
Natural
Whole
Integers
Rational
2,  , e
How many
irrational numbers
are there?
Irrational
Real Number System
Natural
Whole
Integers
Each set is a subset of the
Real Number System.
The union of all these sets
forms the real number
system.
The number line is our model
for the real number system.
Irrational
Rational
Real
Numbers
Interval Notation
Example 1
x 5  3
5  5
x  2
Notice that the
open circle
translates into a
parenthesis.
We can also express this
solution with a graph.
-2
(2, )
A third way to express
this solution is by using
interval notation.
Example 2
1  x  5
We can express this situation with a graph.
-1
5
We can also express this graph with interval
notation.
(1, 5]
Example 3 x  1 or
x5
We can express this situation with a graph.
-1
5
We can also express this graph with interval
notation.
(, 1]  (5, )
Exercise 1 Translate the graph into
interval notation.
-3
5
[3, 5)
Solid circles are brackets.
Open circles are parenthesis.
Exercise 2 Translate the graph into
interval notation.
3
(3, )
Arrows translate into infinity signs with
parenthesis.
Always.
Exercise 3 Translate the graph into
interval notation.
( ,  )
Arrows translate into infinity signs with parenthesis.
Negative infinity always goes to the left.
Positive infinity always goes to the right.
Exercise 4 Translate the graph into
interval notation.
-8
10
(, 8)  (10, )
An open circles is always a parenthesis.
Negative infinity always goes to the left.
Positive infinity always goes to the right.
P.1 Determine which numbers are (a)
natural numbers, (b) integers, (c) rational
numbers, and (d) irrational numbers.
7 2
9, ,5, , 2, 0,1, 4, 1
2
3
In exercises 25-34, (a) verbally describe the subset of real
numbers represented by the inequality, (b) sketch the
subset on the real number line and (c) state weather the
interval is bounded or unbounded
x4
In exercises 37 – 47, use inequality and
interval notation to describe the set.
p is less than 8 but no less than -1.
P.1 Assignment
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•
•
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P.1 assignment page 9
1 – 5 all
25 – 34
37- 47 odd
97 – 101