Real Number System.

Prior to understand “Real Numbers” we need to understand the concept of Number system.

So ,

What is Number?

Number is one of the basic concept of mathematics. A Number basically representation of quantity of any object. Number system started from the time of ancient civilization , Primitive man used to compare one quantity with another when there was no number ; Like they used to lay aside each pebble for a sheep they rear , in order to count sheep.  latter with advancement in language they gave the number a name and a symbol like for first quantity the name is “One”  and symbol is “1″ and for fifth quantity the name is “Five” and symbol is “5″.

Each civilization had its own  name and symbols for numbers , among them the most popular one now is “Hindu Arabic” numbering system which has 10 base (or this number system has 10 basic symbols for numbers).

The ten symbols used in “Hindu Arabic” numbering system for numbers are:

0, 1 , 2 , 3 , 4, 5 , 6 , 7 , 8 , 9

Note:

> In 10 base numbering system the higher number are represented by the combination of two or more number symbols to form a single number symbol liker to represent Ten  we combine “1″ and “0″ to form “10″ which means Ten.

> The set of numbers 1,2,3,4…. where each number has a successor is known as “Natural Numbers”

> Zero “0″ symbolizes no quantity.

In the course of time humans discovered other complex types of numbers like Negative  Numbers ; which developed after the concept of negative quantity or debt , Rational (Fractional) Numbers , Irrational (Non-fractional) Numbers.

So now,

What is Real Number?

The collection of sets of following types of numbers is known as real number.

a.  Natural Numbers.

Example: 0,1,2…….10,11,12……..100,101,102………

b. Integers.

Example:

Negative:………….-3,-2,-1

Zero: 0

Positive: 1,2,3………………

c. Rational Numbers.

Example: 0/1 , -1/2 , 3/4 , 12/-4………………….

d.Irrational Numbers.

Example: √2 , √3 , 3√3 , Π

We can also show the above relation between other types of numbers and Real Number diagrammatically by the following diagram: