INTRODUCTION
Mathematics originated from the process of expressing quantities in symbols or numbers. these
numbers play important roles in our daily interactions. Have you ever heard the proverb “necessity
is the mother of invention”? The construction of the real number system is a testimony to this
proverb. Each type of the real numbers was invented to meet a particular purpose. For example,
natural numbers were devised for counting, negative numbers were needed for describing debts
and below zero temperatures. Also, rational numbers were necessary for describing part of a whole
(e.g., half of a mile) while the length of the diagonal of a square gave rise to irrational numbers.
We begin this chapter by reviewing the types of numbers that make up the real number system.
Natural numbers
The first numbers that we learned as children and probably the first numbers used by humankind
are the natural numbers. Natural numbers (also known as counting numbers) are the numbers that
we use to count. It starts from 1, followed by 2, then 3, and so on. The letter ℕ is used to represent
the set of natural numbers. Thus ℕ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, … }
Whole Numbers
The set of whole numbers includes zero and all the natural
numbers. The set of whole numbers is denoted by the letter
𝑾. That is 𝑾 = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9 … }
