SETS
Resources & Insights

A set that has a definite number of elements is called a finite set else it is called an Infinite set. ⇒ A null set is a finite set. ⇒ For finite set S, n(S) is a finite number. ⇒ The standard mathematical sets like N, Z, R, etc. are all infinite. READ MORE...

A set that has exactly one member is called a singleton set. { 1 } , { ‘a’ } , { x3 | x ∈ N , 2 < x < 3 } are all singleton sets. READ MORE...

A set that does not have any members is called an empty set. ⇒ Such sets are represented as {} or using the symbol ∅ (derived from Φ) which has been explicitly developed to designate an empty set. ⇒ Sometimes { ∅ } is also used to designate an empty set. ⇒ An empty set is also called a Void set. ⇒ The cardinality of an empty set is 0. READ MORE...

The number of elements in a set is called cardinality. The cardinality of a set A is generally represented by |A| or n(A) meaning the number of elements in set A.  Examples: The cardinality of the set { 1, 45, 2, 34 } is 4. The cardinality of the set { a, e, i, o, u } is 5. The cardinality of the set { x | x ∈ N } is infinite ( a very large number whose value cannot be determined ) READ MORE...

The position of elements in a set does not change the value or the meaning of the set. The above statement signifies that { 1, 2, 3 } and { 1, 3, 2 } and { 2, 3, 1 } are all the same set. A set is primarily a collection and not a sequential representation of elements. It represents a group as a whole. The {} representation just shows the group in an expanded form. By re-arranging the members of a set, you do not change the group. Just like rearranging the seating position of students makes no changes to the class as a whole (it still contains the same students) or transferring books from one shelf to another […] READ MORE...

As defined earlier, a set is a collection or group of objects. These objects are called members of the Set. This relationship is represented by using the symbol ∈. The symbol ‘∈’ means “is a member of ” or “belongs to” or “is an element of”. The reverse of this relationship is denoted using the symbol ‘ ∋‘. ∋ means “contains as a member“. If V represents the collection of all vowels in the English language, then ‘a’, ‘e’, ‘I’, ‘o’, ‘u’ are all members of this set. We can, hence, write, ‘a’ ∈ V ‘e’ ∈ V ‘i’ ∈ V ‘o’ ∈ V ‘u’ ∈ V We can also write V ∋ ‘u’ Similarly, ∉ and ∌ are used to denote the negation of the membership. ∉ means “is […] READ MORE...

In mathematical terms, the members of sets are called elements. A set is represented by enlisting its member elements within curly brackets. There are three general conventions adopted for set representation – Roster, Ellipsis & Set-Builder form. Roster form {a,b,c} All elements are listed within curly brackets. When the number of elements is less, it is often convenient to list all of them within brackets. Ellipsis (…) form This form uses the ellipsis notation (3 dots) to represent a series of numbers that appear in a sequence and whose next element is obvious from the pattern or has been explicitly specified in the set definition and is easily understood. The last element can be specified for the finite set or be unspecified in case the set […] READ MORE...