**Number system in set theory**, Natural number is denoted by **capital N**, whole number is denoted by **W**, set of integer is denoted by **Z**, Rational number is denoted by **Q**, irrational number is denoted by **Q’**, Real number is denoted by **R** and complex number is expressed as **Z = a+ι b**, all these numbers of definition in detail one by one.

**(1) Natural number definition:**

The number start from one up to undefined, and** complete number**

not a** fractional number** and **denoted by capital N.**

**EXAMPLE:**

**N** = one, two, tree, four………………….∞(

in set theory, set of natural number we enclosed in curly bracket {}

**EXAMPLE:**

**N**= {1,2,3,4…………………………∞ {, this means undefined is not in the set of natural number.

**Whole number definition:**

the number start from Zero up to undefined, and complete number

not a fractional number and denoted by capital W.

**EXAMPLE:**

W =zero, one, two, tree, four………………….∞(

in** set theory**, set of Whole number we** enclosed** in curly bracket** {}**

in set theory, set of natural number we** enclosed **in curly **bracket {}**

**EXAMPLE:**

W= {0,1,2,3,4…………………………∞( this means undefined is not in the set of Whole number.

**EXAMPLE:**

Set of first five whole number = {0,1,2,3,4} in this set zero count as whole number.

**Set of integer definition:**

the number which has positive and negative direction to undefined (∞) and numeric number

has complete number and denoted by capital Z is called set of integer number.

**EXAMPLE:**

**Z**=}…………….-3,-2,-1,0.+1,+2,+3,………..∞{

**Also expressed as**

**Z= 0±1±2±3……………..∞(**

Set of rational number definition:

The numbers which has positive and negative direction to undefined and with all fractional rounding number, denoted by capital Q.

**EXAMPLE:**

Q =}∞, …….-2,…-1.5,….-1,…..-0.5,…0,……+0.5,…… +1,….+2,…….∞{

**Real number definition:**

All numbers without iota is called** real number** and its number

is denoted by capital** R.** in other words, real number is the group

of **all natural, whole, set of integers, rational and irrational number.**

**EXAMPLE:**

**R = N ∪ W ∪ Z ∪ Q ∪ Q’**

means

**Real numbers= Natural ∪ Whole ∪ set of integers ∪ rational ∪ irrational number**

**Complex number definition:**

All numeric numbers with iota will be called complex number, in other words the number

which has real and **imaginary part** is called complex number.

**Z = a ± ι b**

** or**

** z= x ± ι y**