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
● Subset
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