# Standard Sets of Numbers

The standard sets of numbers can
be expressed in all the three forms of representation of a set i.e., statement form, roster form, set
builder form.

1. N = Natural numbers

= Set of all numbers starting from 1                       Statement form

= Set of all numbers 1, 2, 3, ………..

= {1, 2, 3, …….}                                                   Roster form

= {x 😡 is a counting number starting from 1}         Set builder form

Therefore, the set of natural numbers is denoted by N     i.e., N = {1, 2, 3, …….}

2. W = Whole numbers

= Set containing zero and all natural
numbers        Statement
form

= {0, 1, 2, 3, …….}                                               Roster form

= {x 😡 is a zero and all natural
numbers}             Set
builder form

Therefore,
the set of whole numbers is denoted by W      i.e., W
= {0, 1, 2, …….}

3. Z or I = Integers

= Set
containing negative of natural numbers, zero and the natural numbers                                                                                                  Statement
form

= {………, -3,
-2, -1, 0, 1, 2, 3, …….}                           Roster form

= {x 😡 is
a containing negative of natural numbers, zero and the natural numbers}                                                                                      Set builder form

Therefore,
the set of integers is denoted by I or Z    i.e., I = {…., -2, -1, 0, 1, 2, ….}

4. E
= Even natural numbers.

= Set of natural numbers, which are
divisible by 2               Statement form

= {2, 4, 6, 8, ……….}                                                          Roster
form

= {x 😡 is a natural number, which are
divisible by 2}           Set builder form

Therefore,
the set of even natural numbers is denoted by E
i.e., E = {2, 4, 6, 8,…….}

5. O = Odd natural
numbers.

= Set of natural numbers, which are not
divisible by 2          Statement form

= {1, 3, 5, 7, 9, ……….}                                                       Roster
form

= {x 😡 is a natural number, which are
not divisible by 2}      Set builder form

Therefore,
the set of odd natural numbers is denoted by O      i.e.,
O = {1, 3, 5, 7, 9,…….}

Therefore, almost every standard
sets of numbers can be expressed in all the three methods as discussed
above.

+