FHMM1014 Chapter 1 Number And Set 1

Centre For Foundation Studies
Department of Sciences and Engineering

FHMM1014 Mathematics I

Chapter 1
Number and Set
FHMM1014
Mathematics I

1

Content
1.1 Real Numbers System.
1.2 Indices and Logarithm
1.3 Complex Numbers
1.4 Set
FHMM1014
Mathematics I

2

1.1 Real Numbers

FHMM1014
Mathematics I

3

Real Numbers
• Let’s review the types of numbers that make up the real number system.

FHMM1014
Mathematics I

4

Real Numbers
i). Natural numbers (also called positive integers).
N = {1, 2, 3,…..} ii). Integers. Natural numbers, their negatives and zero. Z = {……., -3, -2, -1, 0, 1, 2, 3, 4…….}

FHMM1014
Mathematics I

5

Real Numbers iii) Rational numbers are ratios of integers.
• Thus, any rational number
• can be expressed as:

m
Q
n

where m and n are integers and n ≠ 0.

FHMM1014
Mathematics I

6

Real Numbers
Examples are:

1
3

FHMM1014
Mathematics I

3

7

36

17
0.17 
100

7

Real Numbers
If a number is rational, then its corresponding decimal representation is either terminating or non-terminating repeating.
For examples :
1
0.5 (terminating)
2
2
0.66666.... 0.6 (non  terminating repeating) (the bar indicates the digit repeat forever)
3
9
1.285714285714.... 1.285714 (non  terminating repeating)
7

FHMM1014
Mathematics I

8

Real Numbers
There are also real numbers, such as 2 , that can’t be expressed as a ratio of integers.
Hence, they are called irrational numbers.
• Other examples are:

5

FHMM1014
Mathematics I

3

7



2
3
9

Real Numbers
If the number is irrational, the decimal representation is non-terminating non-repeating:

5  2.236067978...
Show that

FHMM1014
Mathematics I

  3.141592654...

2 is irrational.

10

Real Numbers

FHMM1014
Mathematics I

11

Example 1
Identify each number below as an integer, or natural number, or rational number or irrational number. 23
 8, 21, 0, , 0.5381, 7 , 1.5, 2.005, 0.3333, 0.1234,   , 9
9

FHMM1014
Mathematics I

12

Operations on Real Numbers
(i) Commutative Law
* Addition : a