Ch 2.1

Objective:

To recognize different sets of numbers and to identify a domain.

DefinitionsNatural 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 IrrationalsAny number which can be written as a fraction

Non-terminating and non-repeating decimals which can’tbe written as fractions.Examples:

7

2.09

0 3.

=71

=29

100

=13

Real Numbers

Rationals IrrationalsAny number which can be written as a fraction

Non-terminating and non-repeating decimals which can’tbe written as fractions.

Examples:

π ≈3141592. ...

2 ≈1414213. ...

1212112111211112. ...

123456789101112. ...−4 7. =−4

79

Examples:

7

2.09

0 3.

=71

=29

100

=13

Sets of Numbers Reals

Rationals Irrationals- any number whichcan be written as afraction.

2

3, 7, -0.4

Fractions/Decimals Integers

61

4 , -0.32, - 2.1 …-3, -2, -1, 0, 1, 2, 3...

Negative Integers Wholes…-3, -2, -1 0, 1, 2, 3...

Zero0

Naturals1, 2, 3...

- non-terminating and non-repeating decimals

π ≈3141592. ...

2

Make a Venn Diagram that displays the following sets of numbers: Reals, Rationals, Irrationals, Integers, Wholes, and Naturals.

Naturals1, 2, 3...

Wholes0

Integers-3 -19

Rationals2

3

61

4

-2.65

Irrationalsπ2

Reals

Naturals1, 2, 3...

Wholes0

Integers-3 -19

Rationals2

3

61

4

-2.65

Irrationalsπ2

Reals

Imaginary Numbers

−1

Identify all of the sets to which each number belongs.(Reals, Rationals, Irrationals, Integers, Wholes, Naturals)

1) -6

2)

€

−578

3) 14

4) 6π

Integer, Rational, Real

Rational, Real

Natural, Whole, Integer, Rational, Real

Irrational, Real

Identify all of the sets to which each number belongs.(Reals, Rationals, Irrationals, Integers, Wholes, Naturals)

1) 0

2) - 2.03

3)

4)

Whole, Integer, Rational, Real

Rational, Real

Irrational, Real

Integer, Rational, Real

2 3

€

−10

€

−112

Graphing Real Numbers on a Number Line

Graph the following numbers on a number line.

€

−3

€

−112

€

53

€

−0.4

€

π

-4 -3 -2 -1 0 1 2 3 4

€

−3

€

53

€

−0.4

€

π

Domain- the set of values which may bemeaningfully 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 weightD: y Positive Reals∈

3) Let t = the low temperature in Alaska yesterdayD: t Reals∈

4) Let n = the low recorded temperature in Alaska.

D: n Integers∈