NUMBER SYSTEM

NUMBER SYSTEM

1. NATURAL NUMBERS OR COUNTING NUMBERS:

1 ,2 ,3 ,4, 5 ,…..∞ are known as natural numbers.

2. WHOLE NUMBERS

0 ,1 ,2 ,3 ,4 ,5 ,…..,∞ are known as whole numbers

3.  INTEGERS:

- ∞ ,….. ,-3 , -2 ,-1,0 , +1,+2 ,+3 ,…..+ ∞

are known as Integers.

POSITIVE INTEGERS:    +1,+2 ,+3 , +4, +5…..+ ∞

NEGATIVE INTEGERS:   -1 ,-2 ,-3 , -4 ,-5 ,….. , - ∞

                                ZERO : neither positive nor negative integer.

4.   RATIONAL NUMBERS: NUMBERS OF THE FORM                                                                                                                                                                                                                  

      Numbers: of the form p/q  where q≠0   and p, q are integers .

       Examples : 2/3 ,5/7, 11/17 , -2/3 , -5/4 , 2 ,6 ,0 ,-2 ,-9 ,

       Note (a)  All terminating decimals are rational

        0.5, 0.125 ,  0.7 , 0.213 0867 ,  0.9

       

      Note (b )    All  non-terminating  ,but recurring  decimals are rational

                        0.33333....; 0.77777 , …., 0.123123123,….

                0.2561725617……, 0.521212121…..

     5. IRRATIONAL NUMBERS : numbers that are  not rational are known as  

        irrational . (Numbers that can not be expressed as p/q form )

Examples: √2, √5, √7, √11, -√3,-√5 , ……

      6. Real Numbers: Union of Rational and Irrational Numbers.

Examples: 5, 7, -3, 0, ⅔, 0.5, 1.67, 0.3333………,

                   √2, √5, ╥, e, -√11, 2/5 , ……….

         7. Imaginary Numbers: Numbers that are not real are imaginary.

                                                   i=√-1                i²  = -1

                i , -i , 2i , - 3i , 7i

      8. Complex Numbers : Combination of real and imaginary numbers.

                 Numbers of the form  : a + i b ,

                                                                               where a and b are real numbers i is imaginary number.

Examples :  2 + 7i , 5 – 3i , 2i , -4i , i , 6 + 11 i