A number system is a writing system for expressing numbers; it is a way to represent quantities and perform mathematical operations. The number system consists of a set of symbols (digits) and rules for combining these symbols to represent numbers. The most common number systems include the decimal system, binary system, octal system, and hexadecimal system.
2. Types of Number Systems
2.1. Natural Numbers
Definition: Natural numbers are the set of positive integers used for counting. They start from 
and go on indefinitely.
Symbol: The set of natural numbers is denoted by 
.
Example:
![\[ \mathbb{N} = \{1, 2, 3, 4, 5, \ldots\} \]](https://www.sridianti.com/wp-content/uploads/2025/07/quicklatex.com-660d4277d319c9ffc2f87717049ceee9_l3.png "Rendered by QuickLaTeX.com")
Illustrative Explanation: Natural numbers are used in everyday counting scenarios, such as counting apples, people, or any discrete items. For instance, if you have 
apples, you can represent this quantity using the natural number .
2.2. Whole Numbers
Definition: Whole numbers include all natural numbers along with zero. They are non-negative integers.
Symbol: The set of whole numbers is denoted by 
.
Example:
![\[ \mathbb{W} = \{0, 1, 2, 3, 4, 5, \ldots\} \]](https://www.sridianti.com/wp-content/uploads/2025/07/quicklatex.com-fe608722064b0e743d843902509255de_l3.png "Rendered by QuickLaTeX.com")
Illustrative Explanation: Whole numbers are useful in scenarios where zero is a valid quantity. For example, if you have no apples, you can represent this quantity using the whole number 
.
2.3. Integers
Definition: Integers include all whole numbers and their negative counterparts. They can be positive, negative, or zero.
Symbol: The set of integers is denoted by 
.
Example:
![\[ \mathbb{Z} = \{\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots\} \]](https://www.sridianti.com/wp-content/uploads/2025/07/quicklatex.com-f5388f350c65af1ac2270a4be619c917_l3.png "Rendered by QuickLaTeX.com")
Illustrative Explanation: Integers are used in various contexts, such as temperature measurements (where temperatures can be below zero) or financial transactions (where losses can be represented as negative integers).
2.4. Rational Numbers
Definition: Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. They can be positive, negative, or zero.
Symbol: The set of rational numbers is denoted by 
.
Example:
![\[ \mathbb{Q} = \left\{ \frac{1}{2}, -\frac{3}{4}, 0, 2, 5.5 \right\} \]](https://www.sridianti.com/wp-content/uploads/2025/07/quicklatex.com-bc160c2cc7d37e8932c3de31960ad498_l3.png "Rendered by QuickLaTeX.com")
Illustrative Explanation: Rational numbers are used in situations where quantities are not whole numbers. For example, if you have half a pizza, you can represent this quantity as the rational number 
.
2.5. Irrational Numbers
Definition: Irrational numbers are numbers that cannot be expressed as the quotient of two integers. They have non-repeating, non-terminating decimal expansions.
Symbol: The set of irrational numbers is denoted by 
.
Example:
![\[ \mathbb{I} = \{\sqrt{2}, \pi, e\} \]](https://www.sridianti.com/wp-content/uploads/2025/07/quicklatex.com-ee35c78422e278ddd5f83c0bf27d8491_l3.png "Rendered by QuickLaTeX.com")
Illustrative Explanation: Irrational numbers often arise in geometry and calculus. For instance, the square root of 
is an irrational number because it cannot be expressed as a simple fraction, and its decimal representation is approximately 
, which goes on indefinitely without repeating.
2.6. Real Numbers
Definition: Real numbers include all rational and irrational numbers. They can be represented on the number line.
Symbol: The set of real numbers is denoted by 
.
Example:
![\[ \mathbb{R} = \{\ldots, -3, -2.5, -1, 0, 1, 2.5, 3, \sqrt{2}, \pi, \ldots\} \]](https://www.sridianti.com/wp-content/uploads/2025/07/quicklatex.com-c0df0c6341c1b8d627baaaf037d36a3a_l3.png "Rendered by QuickLaTeX.com")
Illustrative Explanation: Real numbers encompass all possible quantities that can be measured. For example, the height of a person can be represented as a real number, such as 
meters.
2.7. Complex Numbers
Definition: Complex numbers are numbers that consist of a real part and an imaginary part. They are expressed in the form 
, where 
and 
are real numbers, and 
is the imaginary unit defined as 
.
Symbol: The set of complex numbers is denoted by 
.
Example:
![\[ \mathbb{C} = \{3 + 2i, -1 - i, 0 + 4i\} \]](https://www.sridianti.com/wp-content/uploads/2025/07/quicklatex.com-e422bab5bec1a806bc7899942c03cbb3_l3.png "Rendered by QuickLaTeX.com")
Illustrative Explanation: Complex numbers are used in advanced mathematics, engineering, and physics. For instance, in electrical engineering, complex numbers are used to analyze alternating current (AC) circuits.