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Chapter 1C - Sets and Venn Diagrams Chapter 1C - Sets and Venn Diagrams A Set is a collection of objects. Elements of the set are the individual objects, e.g., if x is an element of a set S then we write x ∈ S . Sets are described by listing their members within }. Use three dots,. . ., to indicate a continuing pattern if there are too a pair of braces, { A Set is a collection of objects. Elements of the set are the individual objects, e many members to list. element of a set S then we write x ∈ S . Sets are described by listing their mem - Sets braces, { }. Use Diagrams Venn Diagrams Chapter 1C a pair of andand of Numbers dots,. . ., to indicate a continuing pattern if t Chapter 1C - Sets Sets Venn three many members to list. Chapter 1C - Sets and Venn Diagra of objects. Elements (counting numbers) et is a collection 1. Natural Numbers of the set are the individual objects, of Numbers is an Sets e.g., e.g., if x A Set is a collection of objects. Elements of the set are the individual objects, if x is an {1, 2,write x ∈ S . Sets A Set is a collection of objects. Elements of the set are the individual 3, . . .} (N) ment of a set a set S then we write x ∈ S . Setsdescribed by listing their their members within element of S then we are are described by listing members within }. }. Use dots,. ., 1, indicate a a a S then we write x ∈ . are a of braces, { 2. Whole Numbers. {0,to 2, to indicate setcontinuing pattern if SareSets too element air pair of braces, { Use threethree dots,. . ., 3, . . .} of continuing pattern if theretheretoo are described by listing y members to list. list. 1. Natural Numbers (counting numbers) . ., to indicate a continuing p a pair of braces, { }. Use three dots,. many members to {1, 2, 0, . 2, . .} (Z) 3. Integers {. . . , −3, −2, −1,3, .1,.} 3, .(N) to list. many members of Numbers SetsSets of Numbers x 4. Rational NumbersWhole Numbers0{0, 1,(Q)3, . . .} 2. : x, y ∈ Z y = 2, Sets of Numbers y 3. Integers {. . . −2, . Natural Numbers (counting numbers) numbers , −3,have −1, 0, 1, 2, 3, . . .} (Z) Numbers (counting numbers) 1. Natural 5. Irrational Numbers are that non- 1. {1, 2,{1,.2,.} . . .} repeating and non-terminating Natural Numbers (counting numbers) 3, . 3, (N) (N) decimal expansion. √ 4. Rational {1, 2, 3, . .} x : Examples are 2, base for natural log .e ≈ y(N)x, y ∈ Z y = 0 Numbers 2.7, (Q) . Whole Numbers {0, 1,{0,3, .2,.} . . .} 2. Whole Numbers 2, 1, . 3, π ≈ 3.14. (I) 2. Whole Numbers {0, 1, 2, 3, . . .} ,{. . . ,−2, −1, 0, 1, 2,5. .2,.} . of.} Numbers irra- . Integers {. . . 6. Real Numbers0,3, Irrational rational and are numbers that have non- 3. Integers −3, −3, −2, −1, 1, . 3, . (Z) (Z) consist all 3. and non-terminating decimal expansion. repeating Integers {. . . , −3, −2, −1, 0, 1, 2, 3, . . .} (Z) √ tional numbers. (R) x x Examples are 2, base for natural log e ≈ 2.7, 4. Rational Numbers : x, y: ∈ Zπy≈Z3.14. 0(Q) (Q) . Rational Numbers x, y ∈= 0 = (I) y y y Relationship among Sets x : x, y ∈ Z y = 0 4. Rational Numbers (Q) y 5. Irrational Numbers B numbers have non- Numbers and are 6. that Numbers consist of all rational and irra- . Irrational Given sets Aare numbers Realthat have non- 5. Irrational repeating and non-terminating decimal expansion. A(R) Numbers are numbers that have non- A ⊂ B every numbers. repeating √ non-terminating tional element of is an element of B and Subset √ decimal expansion. Examples 2, 2, forA ∪ B natural e consisting of and element of A and decimal expansion. Examples are are base base naturalthe setlog repeatingevery non-terminating every element of B Union for log ≈ e2.7, 2.7, ≈ √ π ≈ 3.14. 3.14. (I) π≈ (I) Examples are Relationship among Sets≈ 2.7, 2, base for natural log e Interesection A ∩ B the set of all≈ 3.14. in both A and B π elements (I) 6. Numbers . RealReal Numbers ∅ of all sets and irra- empty consist of all rational A and Bno elements set consistGiven set containing irra- rational and tional numbers. sets A and B we have tional numbers. (R) (R) 6. Real Numbers consist of all rational and irra- Given Subset A ⊂ B every (R) tional numbers. element of A is an element of B Relationship among SetsSets Relationship among Union A ∪ B the set consisting of every element of A and every el Relationship among Sets en sets A and B B Interesection A ∩ B the set of all elements in both A and B Given sets A and empty set B Given sets A andset containing no elements ∅ bset Subset A ⊂ A ⊂ every element of A of anis an element of B B B every element is A element of B ion Union A ∪ B ∪ B set consisting of Subsetelement ofA ⊂ B every element ofof A is an element of B every A and every element B A the the set consisting of every element of A and every element of B A A the the set elements in both A andAand Union ∪ B the set consisting of every element of A an Interesection ∩ B ∩ B set of allof all elements in both A B B eresection pty set set ∅ Interesection A ∩ B the set of all elements in both A and B empty ∅ set containing no elements set containing no elements empty set ∅ set containing no elements If A and B have no elements in common we write A ∩ B = ∅ and we say that A and B are disjoint.

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posted: | 4/24/2009 |

language: | English |

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