Algebra 1 Section 1.1

Definitions Set: a collection of objects Element or Member: each object in a set Empty or Null Set: a set with no elements

Symbols Empty set: { } or Ø Element:  Not an element: 

Definitions Union of sets: the set of elements that appear in any of the sets Symbol: 

Definitions Intersection of sets: the set of elements common to all of the sets Symbol: 

Venn Diagram Represents sets in picture form

Venn Diagram C = {1, 2, 3, 4, 5, 6} D = {2, 4, 6, 8, 10}

Venn Diagram C = {1, 2, 3, 4, 5, 6} D = {2, 4, 6, 8, 10} C D 1 8 2 3 4 10 5 6

Venn Diagram C = {1, 2, 3, 4, 5, 6} D = {2, 4, 6, 8, 10} C D C  D 1 8 2 3 4 10 5 6

Venn Diagram C = {1, 2, 3, 4, 5, 6} D = {2, 4, 6, 8, 10} C D C  D 1 8 2 3 4 10 5 6

Definitions One set is a subset of another set if every element of the first is contained in the second Symbol:  A  B: “A is a subset of B” B A

Example 2 a. {5, 6}  C b. C  D  C c. Ø  C d. C  C e. 6  D f. C  D  D True False

Number Sets Natural Numbers N = {1, 2, 3,...} Whole Numbers

Definitions Finite set: the number of elements is a whole number Infinite set: a set that is not finite

Number Sets Natural Numbers N = {1, 2, 3,...} Whole Numbers Integers Z = {...-3, -2, -1, 0, 1, 2, 3,...}

Number Sets N  W N  W  Z

Number Sets Rational numbers are numbers that can be written as a ratio of two integers when the denominator is not equal to zero Q = a  Z, b  Z, and b  0 a b

Number Sets The set of Irrational numbers, Q (“Q prime”), consists of numbers that cannot be expressed as a ratio of integers

Example 3 a. 5 b. 9 c. 6 d. 3.14159 Rational Irrational

Example 3  4 e. f. 0.16 g. 0.121122111222 Irrational Rational

Number Sets The set of Real numbers, R, is the union of the sets of rational (Q) and irrational (Q) numbers This course deals only with the real number system N  W  Z  Q

Homework: pp. 5-6