Number System..

NATURAL NUMBER: The natural (or counting) numbers are 1,2,3,4,5,$1,2,3,4,5,$ etc. There are infinitely many natural numbers. The set of natural numbers,$\left\{1,2,3,4,5,\mathrm{...}\right\}$, is sometimes written Nfor short.

WHOLE NUMBER: The whole numbers are the natural numbers together with 0.

INTEGER: The integers are the set of real numbers consisting of the natural numbers, their additive inverses and zero.

$\left\{\mathrm{...},-5,-4,-3,-2,-1,0,1,2,3,4,5,\mathrm{...}\right\}$

The set of integers is sometimes written J$J$ or Z for short.

RATIONAL NUMBERS: The rational numbers are those numbers which can be expressed as a ratio between two integers. Example, 1/2,1/3,1/4...

IRRATIONAL NUMBERS: An irrational number is a number that cannot be written as a ratio (or fraction).  In decimal form, it never ends or repeats. Example, 1.3333333333...

REAL NUMBERS: The real numbers is the set of numbers containing all of the rational numbers and all of the irrational numbers.  The real numbers are “all the numbers” on the number line.  There are infinitely many real numbers just as there are infinitely many numbers in each of the other sets of numbers.  But, it can be proved that the infinity of the real numbers is a bigger infinity. Denoted by R.

COMPLEX NUMBER: The complex numbers are the set {a+ib | 
$a$ and 
$b$ are real numbers}, where i is the imaginary unit. Example, minus value inside the square root.

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