- Submitted By: Adrian-Yeoh
- Date Submitted: 07/11/2016 6:18 AM
- Category: Science
- Words: 3757
- Page: 16

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

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

8

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......