# BASIC MATHEMATICAL CONCEPTS: 1.2 TYPES OF NUMBERS

Below are the types of numbers we have in Mathematics:

** Natural Numbers:** These are set of counting numbers e.g. 1, 2, 3, 4…. They are used to denote positions such as 1

^{st}, 2

^{nd}, 3

^{rd}, 4

^{th}etc. The Natural Number system is denoted by the letter $N$.

__Integers__**:** These are sets of negative and positive whole numbers including zero (0). e.g. … -3, -2, -1, 0, 1, 2, 3,…. The set of integers are denoted by the letter $Z$.

__Rational Numbers__**:** These are sets of numbers that can be represented in the form $\frac{a}{b}$, where $a$ and $b$ are both integers and $b≠0$. E.g. $\frac{5}{1}$, $\frac{1}{2}$, $\frac{10}{2}$, $\frac{2}{1}$…. etc. The set of rational numbers are denoted by the letter $Q$. Furthermore, the set of Rational numbers are numbers that can terminate after some terms and if they do not terminate after some terms, they have repeated block. Example: $\frac{1}{2}=0.5$, $\frac{1}{4}=0.25$, $\frac{26}{7}=3.\underbrace{714285}\underbrace{714285}$ (which has repeated blocks), $\frac{1}{11}=0.\underbrace{09}\underbrace{09}\underbrace{09}\underbrace{09}…$, $\frac{10}{3}=3.333333…$

** Irrational Numbers:** are set of numbers that do not truncate/terminate and do not have repeated block i.e. the decimal digits continues without recurring. Example. $π=3.141592654…$

$√3 = 1.732050…$

$√2=1.414213562…$. The set of Irrational number are denoted by letter $IQ$.

** Real Number System**: Real numbers are set of all possible numbers. It is made up of both the rational and Irrational number system. It is denoted by the letter $R$.

** Complex Number System**: are sets of numbers which are usually of the form $a+ib$ where a, and b are real numbers and $ i=\sqrt{-1}$ is an imaginary number. It is denoted by $C$.

__CLASSIFICATIONS OF REAL NUMBERS:__

** Even numbers:** Even numbers are numbers that can be divided exactly by 2 (i.e. without a remainder). Examples are: 2, 4, 6, 8, 10,… etc.

** Odd numbers:** Odd numbers are numbers that cannot be divided exactly by 2. Examples are: 1, 3, 5, 9, 11,… etc.

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