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Published byTyler Singleton Modified over 5 years ago

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**Sets of Numbers Unions, Intersections, and Venn Diagrams**

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**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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**Intersection and Union of Sets**

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

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Natural Numbers The natural numbers make up the set of all counting numbers. Which of the following are natural numbers? -7 28 6.2 infinity braces indicate set etc.

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Whole Numbers The whole numbers make up the set of natural numbers, plus zero. Which of the following are whole numbers? 13 -3 2/3 6,127

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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

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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

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**Fractions Containing Zero**

0/number = 0 Try in Calculator number/0 = undefined Try in Calculator

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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? … … .378 √2 π

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**Intersection and Union of Sets**

Venn Diagram A diagram used to depict collections of sets and represent their relationships. A B

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**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 . A B A B

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**Finding the Intersection of Two Sets**

Set-builder Notation Find A B 4 5 1 9 3 2 7

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**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

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