## The Number System

What are some basic number types? Generally, mathematician classifies numbers into numerous types. However, the most common classification of numbers are natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, imaginary numbers, and complex numbers. These number types are thoroughly explained in the subsequent sections.

### Natural Numbers

Natural numbers are also called the counting numbers. They are represented by the letter N. They are 1, 2, 3,…, and so on. Natural numbers are further classified into even numbers, odd numbers, prime numbers, and composite numbers.

N = {1, 2, 3, 4, 5, 6, …}

Natural Numbers are the counting numbers, 1, 2, 3,...

#### Even Numbers

Even numbers are those numbers that are divisible by 2. Such numbers always ends with a digit of 0, 2, 4, 6, or 8. These numbers, when divided by 2, divides into two equal parts. For example, 8÷2 = 4 which means 8 is divided into two equal parts Which is 4+4. Always remember that 0 is an even number. Some examples of even numbers are

3842918

38974586

4596584

785478450

7845963212

Even numbers are divisible by 2 and ends with a digit of 0, 2, 4, 6, 8

#### Odd Numbers

Those numbers that are not divisible by 2 are called the odd numbers. Such numbers always ends with a digit of 1, 3, 5, 7, or 9, and they do not divided a number into two equal parts. Some example of odd numbers are

3842917

38974585

4596589

785478451

7845963213

Odd numbers are not divisible by 2 and always ends with a digit of 1, 3, 5, 7, 9

#### Prime Numbers

Those numbers which can be divided, without a remainder, only by itself and by 1 are called the prime numbers. Remember that,

- 0 and 1 are not prime numbers
- 2 is the only even prime number
- no prime number greater than 5 ends with a digit of 5.

Some examples of prime numbers are:

Prime numbers only divide by 1 and themselves

#### Composite Numbers

Natural numbers greater than 1 which are not prime are called the composite numbers. These numbers are opposite to prime numbers. For example,

4, 6, 8, 9, 12, …

Those numbers that are not prime are the composite numbers.

### Whole Numbers

When zero is added to the set of natural numbers, then they are called whole numbers. Every natural number is a whole number and every whole number is a natural number except zero.

W = {0, 1, 2, 3, 4, 5, 6, …}

When natural numbers begins with zero, they are called whole numbers.

### Integers

Natural numbers, their negatives, and zero are called the integers. Integers will always be whole numbers: fractions, decimals, percentages, and exponents can never be integers.

Z or I = {…, -4, -3, -2, -1, 0, 1, 2 , 3, …}

Positive Integers = {1, 2, 3, 4,..}

Negative Integers = {-1 , -2, -3, -4,…}

Non-Negative Integers = {0, 1, 2, 3, 4…}

Whole numbers and their negatives are called the integers.

### Rational Numbers

Those numbers that can be written in the form of p/q, where p and q are integers and q ≠ 0. Rational numbers are denoted by Q.

Q = {4/7, 3/2, 5/8, 0/1, 2/3, …}

When numbers can be written in the form of p/q, q ≠ 0

### Irrational Numbers

Those numbers that cannot be written in the form of p/q, and when expressed in decimals are neither terminating nor repeating are called the irrational numbers. Such numbers cannot be expressed in fractions.

P = {√2, √3, √5, π, …}

When numbers cannot be expressed in fractions, they are irrational numbers.

### Real Numbers

Set of all the rational and irrational numbers are called the real numbers. They include positive and negative numbers along with 0.

### Imaginary Numbers

When the square root of a negative number is taken, then the resulting number will be an imaginary number.0.

√-2, √-3, √-4 …

### Complex Numbers

A combination of real and an imaginary number in the form of (a + bi), where a and b are real while i is an imaginary part.

## Summary of Number Types

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