Lesson 1 – 1 Real Numbers

Advanced Math/Trig

No Calculator!!!

Ch 1.1 – 1.5 TestTuesday 9/15/15

Learning Objective

To understand properties of real numbers

To understand union of sets

To understand intersection of sets

Real (R )

Rational (Q) Irrational (H)

Integers (Z)

Whole (W)

Natural (N)

(…,–2, –1, 0, 1, 2, …)

Terminating or repeating decimal(4, –5, 0.02, 0.3333, ) 11

2

3( 3, , , 7,etc)e

(0, 1, 2, 3, …)

(1, 2, 3, …)

Real Numbers

1, 2, 3… Natural (N)

0, 1, 2, 3… Whole (W)

… –3, –2, –1, 0, 1, 2, 3…Integers (Z)

Real Numbers (R)Irra

tional (H

)…-, 0.222, 1, 2,

Rational (Q)

In which set does each belong?

1. 2

2.

3.

4. 1.6

5. 0.

6. –7

N, W, Z, Q, R

Q, R

H, R

Q, R

Q, R

Z, Q, R

Union & Intersection of Sets

Union of Sets – AB elements in A, in B, or in BOTH include ALL elements (don’t repeat)

Intersection of Sets – A B must be in BOTH A & B only include the elements in both

sets

ExamplesLet R = {real numbers}

H = {irrational numbers}

Q = {rational numbers}

Z = {integers}

W = {whole numbers}

N = {natural numbers}

1, 2, 3… Natural (N)

0, 1, 2, 3… Whole (W)

… –3, –2, –1, 0, 1, 2, 3…Integers (Z)

Real Numbers (R)Irra

tional (H

)…-, 0.222, 1, 2,

Rational (Q)

Find the following1. Z H

2. Z Q

3. N Q

4. N H

5. N W

6. N W

(null set)

Q

Q

(null set)

W

N

A = {0, 2, 3, 4, 6, 9}

B = {0, 2, 4, 6, 8, 10} C = {3,

4, 5, 6}

1. A B

All elements, but don’t repeat

{0, 2, 3, 4, 6, 8, 9, 10}

2. C B

Include elements that are only in BOTH

{4, 6}

A = {0, 2, 3, 4, 6, 9}

B = {0, 2, 4, 6, 8, 10} C = {3,

4, 5, 6}

3. (A B) C

Grouping symbol first!

{0, 2, 3, 4, 6, 8, 9, 10} {3, 4, 5, 6}

{3, 4, 6}

A = {0, 2, 3, 4, 6, 9}

B = {0, 2, 4, 6, 8, 10} C = {3,

4, 5, 6}

4. (A B) C

{0, 2, 4, 6} {3, 4, 5, 6}

{0, 2, 3, 4, 5, 6}

A = {0, 2, 3, 4, 6, 9}

B = {0, 2, 4, 6, 8, 10} C = {3,

4, 5, 6}

5. A (B C)

{0, 2, 3, 4, 6, 9}{0, 2, 3, 4, 5, 6, 8, 10}

{0, 2, 3, 4, 6}

Different than #4!!

A = {0, 2, 3, 4, 6, 9}

B = {0, 2, 4, 6, 8, 10} C = {3,

4, 5, 6}

6. (A B) C

{0, 2, 4, 6} {3, 4, 5, 6}

{4, 6}

Ticket Out the Door

Determine N Z, and EXPLAIN how you came to your conclusion.

Determine N Z, and EXPLAIN how you came to your conclusion

Homework#101 Pg. 9 #1 – 9 odd, 11 – 20 all,

21 – 31 odd