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20 Jun 2018

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 1st, 2nd, 3rd, 4th 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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