Set Theory Basics | Set 01 | Mathematics

What is Set?

⇒ Set is a collection of different well-defined objects.

⇒ Fox Example

    Set A Represented As A={1,2,3,4,5,6}

    ⇒ Here, the name of the set is 'A'.

    ⇒ Elements of the set are represented between curly brackets '{ }'.

    ⇒ Elements of the set are separated by 'Commas(,)'.

    ⇒ Here, " 1,2,3,4,5,6 " are Elements of Set A.

    ⇒ the Same element can be repeated in sets.

⇒ The name of the Set can be anything but generally, it is Capital Alphabet (like A, B, C, etc.).

⇒ Collection of the well-defined object may be Finite or Infinite.

⇒ Sets can be Discrete or Continuous.

Discrete sets

⇒ Discrete sets: All the elements are discrete.A={12,43,56,34,76,8,4,-4}

⇒ Discrete sets are represented by curly bracelets { }.

Continuous sets

⇒ Continuous Sets: Elements of this set is continuous like A is a set of a number between 1 and 2. 

    So, here continuous set A=(1,2).[Note: here '( )' is represented open interval]

    here, set A contains All possible values between 1 and 2.

⇒ Continuous sets are represented by '( )', '[ ]', '( ]', '[ )' intervals.

    where, 

• ( ) is open interval
• [ ] is closed interval
• ( ] is left open - Rigth closed interval
• [ ) is left closed - Right open interval

What is a Finite Set?

⇒ Set which Contains a Finite number of elements.

→ For Example A={1,2,3,4,5,6,7,8,9}

→ Here, A is a Finite Set. (Number of Set A = 9).

What is an Infinite Set?

⇒ Set which Contains an Infinite number of elements.

→ For Example A={1,2,3,......} (A = Set of all natural numbers).

→ Here, A is an Infinite Set. (Number of Set A = ∞).