CLASSIFICATION OF NUMBERS

“MATHEMATICS IS THE QUEEN OF ALL SCIENCES AND NUMBER THEORY IS THE QUEEN OF MATHEMATICS”—-GAUSS

numbers

                             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.

 

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