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
7th Grade Math Problems
From Standard Sets of Numbers to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Apr 17, 24 01:53 PM
Apr 17, 24 01:32 PM
Apr 16, 24 02:00 AM
Apr 16, 24 01:15 AM
Apr 15, 24 11:30 PM