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Section 1.2 & 9.1

Section 1.2 & 9.1. Symbols and Sets of Numbers Compound Inequalities. Symbols and Sets of Numbers. Identify natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. Find the intersection of two sets. Find the union of two sets.

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Section 1.2 & 9.1

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  1. Section 1.2 & 9.1 Symbols and Sets of Numbers Compound Inequalities

  2. Symbols and Sets of Numbers • Identify natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. • Find the intersection of two sets. • Find the union of two sets. Section 1.2 & 9.1

  3. Intersection and Union of Sets • Set • A collection of elements separated by commas and enclosed in {braces}. • {2, 4, 6, 8} • The empty set is the set containing no elements. • Represented by the symbol Ø Section 1.2 & 9.1

  4. Natural Numbers • The natural numbers make up the set of all counting numbers. • Which of the following are natural numbers? • -7 • 0 • 28 • 6.2 • ¾ infinity braces indicate set etc. Section 1.2 & 9.1

  5. Whole Numbers • The whole numbers make up the set of natural numbers, plus zero. • Which of the following are whole numbers? • 13 • 0 • -3 • 2/3 • 6,127 Section 1.2 & 9.1

  6. Integers • The integers are made up of the whole numbers and the negatives of all the natural numbers. • Which of the following are integers? • 5.2 • 5 • -2 • 2/5 • 0 Section 1.2 & 9.1

  7. Rational Numbers • The rational numbers make up the set of all numbers that can be written as a fraction of integers. • In decimal form, rational numbers either terminate or repeat. • Which of the following are rational numbers? • 2/7 • -12 • 0/5 • .137 • -.64 Section 1.2 & 9.1

  8. Fractions Containing Zero • 0/number = 0 • Try in Calculator • number/0 = undefined • Try in Calculator Section 1.2 & 9.1

  9. Irrational Numbers • The irrational numbers are all numbers that cannot be written as a fraction of integers. • In decimal form, irrational numbers never terminate or repeat. • Which of the following are irrational numbers? • .272727… • 6.01364… • .378 • √2 • π Section 1.2 & 9.1

  10. Intersection and Union of Sets • Venn Diagram • A diagram used to depict collections of sets and represent their relationships. Section 1.2 & 9.1

  11. Intersection and Union of Sets • Intersection of Two Sets • The set containing only the elements that appear in both sets. • Represented by the symbol . • Union of Two Sets • The set containing all the elements found in either set. • Represented by the symbol . Section 1.2 & 9.1

  12. Finding the Intersection of Two Sets Set-builder Notation • Find • Find 4 5 1 9 3 2 7 Section 1.2 & 9.1

  13. Symbols and Sets of Numbers • Hierarchy of Numbers • Natural (Counting) • 1, 2, 3, 4, … • Whole • 0, 1, 2, 3, 4, … • Integers • …-3, -2, -1, 0, 1, 2, 3, … • Rational Numbers • Any number that can be expressed as a fraction • 3, ½, 6.333 • Irrational Numbers • Numbers that cannot be expressed as fractions • π, √5 • Real Numbers • The set of all rational and all irrational numbers. mutually exclusive Section 1.2 & 9.1

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