The Real Number System Created by Mrs. Gray 2010.
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Transcript of The Real Number System Created by Mrs. Gray 2010.
The Real Number System
Created by Mrs. Gray
2010
What is the Real Number System?
• The set of all rational and irrational numbers.
• { } indicates a set. (braces)
• All numbers can be classified as rational or irrational.
FYI……For Your Information
• …(ellipsis)—continues without end
• { } (set)—a collection of objects or numbers. Sets are notated by using braces { }.
• Venn diagram—a diagram consisting of circles or squares to show relationships of a set of data.
Real Numbers can be classified as:
• Rational– Fractions (proper, improper and mixed)– Integers (positive and negative numbers)– Whole Numbers – Natural Numbers
• Irrational
Natural Numbers
• Always begin with 1
• {1, 2, 3, 4, 5, 6, 7, . . . .}
• Sometimes referred to as Counting Numbers
This is an ellipse Which means it
Continues.
• {x | x can be written as a decimal number.}
• Read as all numbers x, such that x is a decimal.– Examples
• 3 can be written 3.0• ¼ can be written 0.25• 2 ½ can be written as 2.5• -5 can be written as -5.0
Real Numbers
Whole Numbers
• Always begin with 0
• { 0, 1, 2, 3, 4, 5, . . . . .}
• The set of Whole Numbers is the same as Natural except that it includes 0.
• The way to remember it is think “0” in “whole”
Integers
• The set of all natural numbers and their additive inverses (opposites) and 0.
• {. . . . -3, -2, -1, 0, 1, 2, 3, . . . .}
• Does not include fractions or decimals
Rational Numbers
• Numbers that can be expressed as the ratio (fraction) of two integers, a/b where b ≠ 0.
• Decimal representations of rational numbers either terminate or repeat.
• Examples: – 2.375, can be read as 2 and 375 thousandths and
written as 2 375/1000, (terminating decimal)
– 4, can be written as 16/4, 4/1, 8/2– −0.25, can be read as negative 25 one-hundredths
and written as - 25/100– 0.14, repeating decimal and can be written as 14/99
Irrational Numbers
• Numbers that cannot be expressed as a ratio (fraction) of two integers.
• Their decimal representations neither terminate nor repeat. Decimals that go on forever without repeating a pattern.
• Examples: – 3– 0.14114111411114…
Real Number System
Irrational Numbers Rational Numbers
Integers- +
Whole Numbers“0”
Natural Numbers“Counting”
Fractions
Rational Numbers
Any number that can be written as a fraction a where be can not equal 0. b
IrrationalNumbers
REAL NUMBER SYSTEM
Integers
All Positive Numbers and their opposites
including 0.WholeNumbers
All positive numbers plus 0.
NaturalNumbers
Questions
• Determine if the following statements are true or false and give a short reason why:– Every integer is a rational number.– Every rational number is an irrational number.– Every natural number is an integer.– Every integer is a natural number.