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SETS OF NUMBERSUNIONS, INTERSECTIONS, AND VENN DIAGRAMSSection 10.2 & 18.2

Section 1.2 & 9.1

Symbols and Sets of NumbersIdentify 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

Intersection and Union of SetsSetA 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

Section 1.2 & 9.1

Natural NumbersThe natural numbers make up the set of all counting numbers.

Which of the following are natural numbers?-70286.2 infinitybraces indicate setetc.

Section 1.2 & 9.1

Whole NumbersThe whole numbers make up the set of natural numbers, plus zero.

Which of the following are whole numbers?130-32/3 6,127

Section 1.2 & 9.1

IntegersThe integers are made up of the whole numbers and the negatives of all the natural numbers.

Which of the following are integers?5.25-22/50

Section 1.2 & 9.1

Rational NumbersThe 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?2/7-120/5.137-.64

Section 1.2 & 9.1

Fractions Containing Zero0/number = 0Try in Calculatornumber/0 = undefinedTry in Calculator

Section 1.2 & 9.1

Irrational NumbersThe 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?.2727276.01364.3782

Section 1.2 & 9.1

Intersection and Union of SetsVenn DiagramA diagram used to depict collections of sets and represent their relationships.

Section 1.2 & 9.1

Intersection and Union of SetsIntersection of Two SetsThe set containing only the elements that appear in both sets.Represented by the symbol .Union of Two SetsThe set containing all the elements found in either set.Represented by the symbol .

Section 1.2 & 9.1

Finding the Intersection of Two Sets

Find

Find

1357942Set-builder Notation

Section 1.2 & 9.1

Symbols and Sets of NumbersHierarchy of NumbersNatural (Counting)1, 2, 3, 4, Whole0, 1, 2, 3, 4, Integers-3, -2, -1, 0, 1, 2, 3, Rational NumbersAny number that can be expressed as a fraction3, , 6.333Irrational NumbersNumbers that cannot be expressed as fractions, 5Real NumbersThe set of all rational and all irrational numbers.mutually exclusive

Section 1.2 & 9.1

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