“MATHEMATICS IS THE QUEEN OF ALL SCIENCES AND NUMBER THEORY IS THE QUEEN OF MATHEMATICS”—GAUSS
1.various number systems

natural numbers :numbers 1,2,3,…….used for counting or counting numbers.

zero:0

whole numbers:0,1,2,3,……………….

Negative integers: 1,2,3,4,……….

Integers: ……….3,2,1,0,1,2,3……..

fractions: numbers in the form a/b(b is not equal to 0 or1).

Real numbers:numbers which can represented on areal line.

Imaginary number:Pi;where p is real number and i=square root of 1

complex numbers:numbers in the form a+bi where a and b are reals and i=square root of 1r:.

prime numbers: The number which can be divided evenly only by 1 or itself. And it must be a whole number greater than 1.

composite numbers:A non zero integer which is either a unit nor a prime is called a composite number.

Even numbers:0,+/2,+/4,……..

Odd numbers:+/1,+/3,+/5,…….

Natural numbers:1,2,3,4,………….
2.properties of numbers
a; closure property
where Z1 and Z2 are complex numbers
Z1+Z2=a complex number.
Z1.Z2=a complex number
b;commutative property
z1+z2=Z2+Z1
Z1.Z2=Z2.Z1
c;Associative property
(Z1+Z2)+Z3=Z1+(Z2+Z3)
(Z1.Z2).Z3=Z1.(Z2.Z3)
e;Identity property
z+0=0
z.1=z
f;Inverse property
Z+(Z)=0
Z.Z^1=1(Z is not equal to zero)
g;distributive property
Z1.(Z2+Z3)=Z1.Z2+Z1.Z3.