numb3rs mathscience innovation center. adjectives my pencil point is dull and needs sharpening. wow!...
TRANSCRIPT
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