NUMB3RS

MathScience Innovation Center

Adjectives

• My pencil point is dull and needs sharpening.

• Wow! Look at that one-headed person.

• These cookies are delicious.

When do we need adjectives?

Real Numbers

• Real is an adjective

• Adjectives are only needed when there are other kinds of the same noun that do not fit that description

• So… there must be other numbers that are Not Real Numbers

• What are these numbers called?

Numbers

• Real • (Not Real)

• Imaginary

• Actually are real

• And difficult to imagine

Numbers (in 2005 AD)

• a + b i

Numbers (in 2005 AD)

• a + b i

Numbers (in 2005 AD)• a + b i

5 ½ .7

- 810

Who lives out here?

Numbers (in 2005 AD)• a + b i

5 ½ .7

- 810

Numbers where b is not zero

5 + 3 i

-2 + 7 i½ - 3 i

95 + .43 i

So what is “i” ?

• i= the square root of negative one

• i2 = negative one

• i3= the negative square root of a negative one

• i4= one

1

Numbers (in 2005 AD)• a + b i

Who lives out here?

½ -8.76

33i½ i

-8.76i

i

Numbers (in 2005 AD)• a + b i

Numbers where neither a nor b is zero

½ -8.76

33i½ i

-8.76i

i

Numbers (in 2005 AD)• a + b i

2 + 3i -7 + ½ i

½ -8.76

33i½ i

-8.76i

i

.2 + -.3i

Rational: Q

Irrational: H

½ Rational: Q

3

3

-5½

-75

½

.98543

37

12316

53

0

450.7 Rational: Q

3

3

-5½

-75

½

.98543

450.7

37

12316

53

Rational: Q

3

3

0integer

-75

½

450.7

6

53

Rational: Q

30

integer

-75

½

450.7

6

53

Rational: Q

30

integer

whole

-75

½

450.7

6

53

Rational: Q

30

integer

whole

-75

½

450.7

6

53

Rational: Q

30

integer

whole

-75

½

450.7

6

53

Rational: Q

30

integer

Whole (W)

Natural (N)

Now…let’s change channels

• Make a number tree

• Start with the set zero

• Build up to all numbers

• Include one sample in each branch

Numbers

? ?

? ?

? ?

? ?

? Zero

Numbers

Real R Imaginary I

Irrational H Rational Q

Non-integers Integers Z

Negative Integers Whole Numbers W

Natural or Counting N Zero3

0,3-5

-5,0,3¼

-5,0,¼, 3

-5,0, ¼ ,3, 3i

-5,0, ¼ ,3, , 3i