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 :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 :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 :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 :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 :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.

Set Theory

Sets

Objects Form a Set

Elements of a Set

Properties of Sets

Representation of a Set

Different Notations in Sets

Standard Sets of Numbers

Types of Sets

Pairs of Sets

Subset

Subsets of a Given Set

Operations on Sets

Union of Sets

Intersection of Sets

Difference of two Sets

Complement of a Set

Cardinal number of a set

Cardinal Properties of Sets

Venn Diagrams