REAL NUMBERS - DIFFERENT SETS
OF NUMBERS FORMING THIS SET,
PROPERTIES

Please study

Rational Numbers

and

Irrational Numbers before Real Numbers.





We have

Set of Natural Numbers, N
= {1, 2, 3, ......}

Set of Whole Numbers, W
= {0, 1, 2, 3, ......}

Set of Integers, Z
= {... -3, -2, -1, 0, 1, 2, 3, ...}

Set of Rational Numbers, Q
= {x/x = p⁄q where p, q ∈ Z, q ≠ 0}

Set of Irrational Numbers, Q'
= { All surds and numbers like π, e etc.
which in decimal form are
non-terminating and non-repeating decimals. }

Set of all the above Numbers

Set of Real Numbers, R
= The set comprising of all the above Numbers.

The set R in chart form

The set R in chart form is shown below.

                                                                       
                                                                     
                                                                     
                                               Real Numbers(R)       
                                              ---------------       
                                              ⇓             ⇓   
                                 Rational Numbers(Q)       Irrational Numbers(Q')
                                ------------------
                                ⇓                 ⇓
                             Integers(Z)         Fractions 
                           -------------
                           ⇓            ⇓
                     Whole Numbers(W)   Negative Integers 
                    --------------       
                    ⇓            ⇓   
          Natural Numbers(N)    Zero ('0')

Properties w.r.t. Multiplication and Addition

The properties of different sets of Numbers with respect to Addition and Multiplication are given below in a tabular form.