REAL NUMBER SYSTEM
The concept of numbers is as old as the world
itself. Even the story of creation started
exposing the idea of numbers since we are told
the world was created systematically in a
certain number of days. Since then, most
activities and events in man’s life have resulted
in some form of numbering of a sort. For
example, the naming of children in most
cultures reflect their order of birth. This means
that numbers exist naturally.
,• It can therefore be observed that the first type of
number system in man’s life is the natural
numbers or counting numbers. Then other
activities and events in man’s life resulted in the
expansion of the natural numbers to whole
numbers, integers, rational numbers, and
irrational numbers.
TYPES OF REAL NUMBERS
• NATURAL/COUNTING NUMBERS: They are
numbers which starts from one to positive
infinity. They are also known as positive integers.
,• It is denoted by 𝑁. Thus the set of natural
numbers is written as 𝑁 = 1, 2, 3, 4, … .
• WHOLE NUMBERS: They are numbers
which start from zero to positive infinity. It is
denoted by 𝑊. Thus the set whole numbers is
represented by 𝑊 = 0, 1, 2, 3, … .
• INTEGERS: They are numbers which start
from negative infinity to positive infinity. It is
denoted by 𝑍 . The set of integers is
represented by 𝑍 = … , −2, −1, 0, 1, 2, … .
, • RATIONAL NUMBERS: They are numbers
𝑎
which can be expressed in the form where
𝑏
𝑎, 𝑏 ∈ 𝑍 and 𝑏 ≠ 0 . It is denoted by 𝑄 .
Rational numbers can be express in different
forms. They are:
• Proper Fraction: it is a fraction with the
numerator less than the denominator. That is a
𝑎
rational number in the form , 𝑎 < 𝑏 . For
𝑏
2 3 5
example, , , ,…
5 4 7
• Improper Fraction: it is a fraction with the
The concept of numbers is as old as the world
itself. Even the story of creation started
exposing the idea of numbers since we are told
the world was created systematically in a
certain number of days. Since then, most
activities and events in man’s life have resulted
in some form of numbering of a sort. For
example, the naming of children in most
cultures reflect their order of birth. This means
that numbers exist naturally.
,• It can therefore be observed that the first type of
number system in man’s life is the natural
numbers or counting numbers. Then other
activities and events in man’s life resulted in the
expansion of the natural numbers to whole
numbers, integers, rational numbers, and
irrational numbers.
TYPES OF REAL NUMBERS
• NATURAL/COUNTING NUMBERS: They are
numbers which starts from one to positive
infinity. They are also known as positive integers.
,• It is denoted by 𝑁. Thus the set of natural
numbers is written as 𝑁 = 1, 2, 3, 4, … .
• WHOLE NUMBERS: They are numbers
which start from zero to positive infinity. It is
denoted by 𝑊. Thus the set whole numbers is
represented by 𝑊 = 0, 1, 2, 3, … .
• INTEGERS: They are numbers which start
from negative infinity to positive infinity. It is
denoted by 𝑍 . The set of integers is
represented by 𝑍 = … , −2, −1, 0, 1, 2, … .
, • RATIONAL NUMBERS: They are numbers
𝑎
which can be expressed in the form where
𝑏
𝑎, 𝑏 ∈ 𝑍 and 𝑏 ≠ 0 . It is denoted by 𝑄 .
Rational numbers can be express in different
forms. They are:
• Proper Fraction: it is a fraction with the
numerator less than the denominator. That is a
𝑎
rational number in the form , 𝑎 < 𝑏 . For
𝑏
2 3 5
example, , , ,…
5 4 7
• Improper Fraction: it is a fraction with the
