sets of numbers unions, intersections, and venn diagrams section 10.2 & 18.2
TRANSCRIPT
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SETS OF NUMBERSUNIONS, INTERSECTIONS, AND VENN DIAGRAMS
Section 10.2 & 18.2
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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
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
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Natural Numbers
The natural numbers make up the set of all counting numbers.
Which of the following are natural numbers?a. -7b. 0c. 28d. 6.2e. ¾
1,2,3,4,5,...,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?a. 13b. 0c. -3d. 2/3 e. 6,127
0,1,2,3,4,5,...,
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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?a. 5.2b. 5c. -2d. 2/5e. 0
,..., 3, 2, 1,0,1,2,3,...,
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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?a. 2/7b. -12c. 0/5d. .137e. -.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?a. .272727…b. 6.01364…c. .378d. √2e. π
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Intersection and Union of Sets
Venn Diagram A diagram used to depict collections of sets and
represent their relationships.
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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
Find
Find
,
If is an odd number greater than 0 and less than 10
and 1,2,3,4
A x x
B
A B
A B
1,3
1,2,3,4,5,7,9
1
3
5
7
94
2
1,3,5,7,9Set-builder Notation
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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