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