Centre For Foundation Studies
Department of Sciences and Engineering
FHMM1014 Mathematics I
Chapter 1
Number and Set
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Contents
1.1 Real Numbers System
1.2 Indices and Logarithm
1.3 Complex Numbers
1.4 Set
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1.1 Real Numbers
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Real Numbers
What number system have you been using most of
your life?
The real number system.
A real number is any number that has a decimal
representation.
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Set of Real Numbers
(i) Natural Numbers
Counting numbers (also called positive integers)
N = { 1, 2, 3, …… }
Whole Numbers:
W {0} N {0,1, 2,3,}
(ii) Integers
Natural numbers, their negatives, and 0.
Z = {……, –2, –1, 0, 1, 2, ……}
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Set of Real Numbers
(iii) Rational Numbers, Q
Numbers that can be represented as a b ,
where a and b are integers and b 0.
All rational number can be represented by:
(a) terminating decimal numbers
such as 5 2 2.5, 1 2 0.5, 3 4 0.75
(b) non-terminating repeating decimal numbers
such as 2 3 0.666..., 2 15 0.1333...
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Set of Real Numbers
(iv) Irrational Numbers
Numbers which cannot be expressed as a ratio of
two integers. They are non-terminating & nonrepeating decimal numbers.
I 2 , e , ,
(v) Real Numbers, R
Rational and irrational numbers.
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Real Numbers
Numbers
Real
Examples of Rational numbers are:
1
3
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7
36
17
0.17
100
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Real
Numbers
Real Numbers
Numbers
Real
1
0.5 (terminating)
2
2
0.66666.... 0.6 (non terminating repeating)
3
(the bar indicates the digit repeat forever)
9
1.285714285714.... 1.285714 (non terminating repeating)
7
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Real Numbers
Numbers
Real
Examples of Irrational numbers are:
5 2.236067978......