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**

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