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
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