Download Objective - To recognize different sets of numbers and to identify a

Ch 2.1
Objective:
To recognize different sets of
numbers and to identify a domain.
Definitions
Natural Number
1, 2, 3, 4, …… (all the numbers you would include if you were to count from 1 to infinity)
Whole Number
0, 1, 2, 3, 4, ….. (all of the natural numbers and 0)
Integer
-2, -1, 0, 1, 2, ……All of the whole numbers including positive numbers, negative numbers, and zero.
Keep in mind that fractions are not integers.
Rational Number
-2/7, -1/2, 0/3, 4/5, 3/1………Any number which can be written as a fraction.
Irrational Number
Any number which can NOT be written as a fraction (a non-terminating & non-repeating decimal)
Real Number
-2, -1, -1/2, 0, ½, 1, 2, ………All of the Integers plus all of the fractions in between the whole numbers.
Note: there are a few exceptions to this but you will learn about these numbers later.
Positive Number
½, 1, 2, 100, ………….A number greater than 0. In other words, if x > 0, then x is a positive number.
Negative Number
-1/2, -1, -2, -100, ………A number less than zero. In other words, if x < 0, then x is a negative number.
Real Numbers
Rationals
Any number which can
be written as a fraction
Examples:
7
7 
1
9
2.09  2
100
1
0. 3 
3
Irrationals
Non-terminating and nonrepeating decimals which can’t
be written as fractions.
Real Numbers
Rationals
Any number which can
be written as a fraction
Examples:
7
7 
1
9
2.09  2
100
1
0. 3 
3
7
4. 7  4
9
Irrationals
Non-terminating and nonrepeating decimals which can’t
be written as fractions.
Examples:
  3141592
.
...
.
...
2  1414213
1212112111211112
.
...
123456789101112
.
...
Sets of Numbers
Reals
Rationals - any number which
can be written as a
2
, 7, -0 4 fraction.
3
.
Irrationals - non-terminating

and
 3141592
.
... non-repeating
decimals
2
Fractions/Decimals
1
6 , -0 32, - 2 1
4
.
.
Integers
…-3, -2, -1, 0, 1, 2, 3...
Negative Integers
Wholes
…-3, -2, -1
0, 1, 2, 3...
Zero
0
Naturals
1, 2, 3...
Make a Venn Diagram that displays the following sets of numbers:
Reals, Rationals, Irrationals, Integers, Wholes, and Naturals.
Reals
Rationals
2
3
-2.65
Integers
-3
-19
Wholes
0
Naturals
1, 2, 3...
1
6
4
Irrationals

2
Imaginary Numbers
1
Reals
Rationals
2
3
-2.65
Integers
-3
-19
Wholes
0
Naturals
1, 2, 3...
1
6
4
Irrationals

2
Identify all of the sets to which each number belongs.
(Reals, Rationals, Irrationals, Integers, Wholes, Naturals)
1) -6 Integer, Rational, Real
7
2) 5
8
Rational, Real
3) 14 Natural, Whole, Integer,
Rational, Real
4) 6 Irrational, Real
Identify all of the sets to which each number belongs.
(Reals, Rationals, Irrationals, Integers, Wholes, Naturals)
1) 0
Whole, Integer, Rational, Real
2) - 2.03 Rational, Real
3) 2 3
Irrational, Real
4) 10 Integer, Rational, Real
Graphing Real Numbers on a Number Line
Graph the following numbers on a number line.
3
-4
-3
3
1
1
2
-2
5
3
-1
0
1 0.4
1
2

0.4
1
2
5
3
3

4
Domain- the set of values which may be
meaningfully substituted for a given variable.
Which set of numbers would best describe the variable?
1) Let x = the number of people at a meeting.
D: x  Naturals
“ is a member of ”
2) Let y = your weight
D: y  Positive Reals
3) Let t = the low temperature in Alaska yesterday
D: t  Reals
4) Let n = the low recorded temperature in Alaska.
D: n  Integers