Centre For Foundation Studies
Department of Sciences and Engineering

FHMM1014 Mathematics I

Chapter 1
Number and Set
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Mathematics I

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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

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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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......