NUMBER AND NUMERATION - REAL, NATURAL, INTEGER, RATIONAL, IRRATIONAL - MATHEMATICS

Real number
Natural number
Integer
Rational no
Irrational no

NATURAL NUMBER  
The set of natural number is denoted by N. In mathematics the natural numbers are the ordinary whole numbers used for counting. They are the positive integers.
Regrettably, there seems to be no general agreement about whether to include “zero” in the set of natural numbers. However they are defined as the positive integers which includes (1,2 3, 4, 5, - - - ) are quite different from non-negative integers which include  (0,1,2,3,) and are refereed to as whole numbers. Natural numbers includes (1,2,3,4,5,6,7,8, 9- - -).

RATIONAL NUMBER
A rational number is a number that car be written as a simple fraction with a integer numerator and a non- zero natural number denominator. They are ratios of two integers e.g 1.5  3/2, 2 2/1 are rational numbers. They are of the type P/Q where P and Q are intergers and q is not equal to zero. Every interger is a rational number. The set of all rational numbers is usually denoted by a bold face Q. two different fraction may correspond to the same rations number for e.g 102 and 20 are equal to 1/2 = 2/4.

INTEGERS  
The negative of a positive integer: Negative numbers are usually written with a negative sign ( a minus sign) as an example the negative of 7 is written 07 and 74 (07) = 0 when the set of negative numbers is combined with the set of natural numbers (which includes zero) the result is defined as the set of integer numbers. Also called integers Z also written z, hence the letter Z comes from German Zahl, meaning number; the set of integers from a ring with operations addition and multiplication.

REAL NUMBERS
Real numbers include the rational and the irrational numbers, phes the decimal numbers. Real numbers can be displayed on a horizontal line with arrow at the edge called the number line. Real numbers are denoted by the letter R. 
IRRATIONAL NUMBERS
These are numbers which cannot be written on the form P/Q. Some of the irrational numbers are           2            3,         Ã± there is no specific symbol for irrational numbers.
IMPORTANT NUMBERS SYSTEM
N         = > natural 0, 1, 2, 3, 4 - - -  or 1, 2, 3, 4, - - - -
Z          => Intergers - - - - - 5, - 4 3, 2, - 1 or
                                                     1, 2, 3, 4, 5,
- => Positive 1, 2, 3, 4, 5 - - - -

INTEGERS 
Q = Rational a/b where a and b are integers and b is not zero
R = Real the limit of a convergent sequence of rational number
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