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

7th Grade Math Problems

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