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.