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Sets of Numbers Unions, Intersections, and Venn Diagrams

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.

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

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.

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

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

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

Fractions Containing Zero
0/number = 0 Try in Calculator number/0 = undefined Try in Calculator

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

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

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

Finding the Intersection of Two Sets
Set-builder Notation Find A B 4 5 1 9 3 2 7

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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