Transcript Ch1-Section 1.2

§ 1.2
Symbols and Sets of
Numbers
Set of Numbers
• Natural numbers – {1, 2, 3, 4, 5, 6 . . .}
• Whole numbers – {0, 1, 2, 3, 4 . . .}
• Integers – {. . . –3, -2, -1, 0, 1, 2, 3 . . .}
• Rational numbers – the set of all numbers that can
be expressed as a quotient of integers, with
denominator  0
• Irrational numbers – the set of all numbers that
can NOT be expressed as a quotient of integers
• Real numbers – the set of all rational and irrational
numbers combined
Martin-Gay, Beginning and Intermediate Algebra, 4ed
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Equality and Inequality Symbols
Symbol
a=b
ab
a<b
a>b
ab
ab
Meaning
a is equal to b.
a is not equal to b.
a is less than b.
a is greater than b.
a is less then or equal to b.
a is greater than or equal to b.
Martin-Gay, Beginning and Intermediate Algebra, 4ed
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The Number Line
A number line is a line on which each point is
associated with a number.
–5 –4 –3 –2 –1
– 4.8
Negative
numbers
0
1
2
3
4
5
1.5
Positive
numbers
Martin-Gay, Beginning and Intermediate Algebra, 4ed
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Order Property for Real Numbers
For any two real numbers a and b, a is less than b if a is to the left of
b on the number line.
• a < b means a is to the left of b on a number line.
• a > b means a is to the right of b on a number line.
Example
Insert < or > between the following pair of numbers to make a true
statement.
7
0 
8
Martin-Gay, Beginning and Intermediate Algebra, 4ed
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Absolute Value
The absolute value of a real number a, denoted by |a|,
is the distance between a and 0 on the number line.
| – 4| = 4
Symbol for
absolute
value
|5| = 5
Distance of 4
–5 –4 –3 –2 –1
Distance of 5
0
1
2
3
4
5
Martin-Gay, Beginning and Intermediate Algebra, 4ed
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