When we usually hear about the word Set,the first thing that would come to our mind would be a collection of something.In Mathematics, the basic meaning of set is a "well-defined collection of definite objects is called a set."
George Cantor is regarded as the "Father of Set theory".
The concept of "Sets" is basic in all branches of mathematics.
Set: Definition: well-defined collection of distinct objects is called a set.Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics.
Notation of Sets: Capital letters are usually used to denote or represent a set.
Representation of Sets: There are two methods of representing a set. (i) Roster Method (ii) Set builder form.
Finite and Infinite Sets: A set is finite if it contains a specific number of elements. Otherwise, a set is an infinite set.
Null Set or Empty Set or Void Set: A set with no elements is an empty set.
Singleton Set or Singlets: A set consisting of a single element is called a singleton set or singlet. The cardinality of the singleton set is 1.
Equivalent Sets: Two finite sets A and B are said to be equivalent sets if cardinality of both sets are equal i.e. n (A) = n (B).
Equal Sets: Two sets A and B are said to be equal if and only if they contain the same elements i.e. if every element of A is in B and every element of B is in A. We denote the equality by A = B.
Cardinality of a Set A: The number of elements in a finite set A, is the cardinality of A and is denoted by n(A).
Universal Set: In any application of the theory of sets, the members of all sets under consideration usually belong to some fixed large set called the universal set.
Subsets: If A and B are sets such that each element of A is an element of B, then we say that A is a subset of B and write A Í B.
Power Set: The family of all subsets of any set S is called the power set of S. We denote the power set of S by P (S).
Hope you like the above example of Sets.Please leave your comments, if you have any doubts.
George Cantor is regarded as the "Father of Set theory".
The concept of "Sets" is basic in all branches of mathematics.
Set: Definition: well-defined collection of distinct objects is called a set.Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics.
Notation of Sets: Capital letters are usually used to denote or represent a set.
Representation of Sets: There are two methods of representing a set. (i) Roster Method (ii) Set builder form.
Finite and Infinite Sets: A set is finite if it contains a specific number of elements. Otherwise, a set is an infinite set.
Null Set or Empty Set or Void Set: A set with no elements is an empty set.
Singleton Set or Singlets: A set consisting of a single element is called a singleton set or singlet. The cardinality of the singleton set is 1.
Equivalent Sets: Two finite sets A and B are said to be equivalent sets if cardinality of both sets are equal i.e. n (A) = n (B).
Equal Sets: Two sets A and B are said to be equal if and only if they contain the same elements i.e. if every element of A is in B and every element of B is in A. We denote the equality by A = B.
Cardinality of a Set A: The number of elements in a finite set A, is the cardinality of A and is denoted by n(A).
Universal Set: In any application of the theory of sets, the members of all sets under consideration usually belong to some fixed large set called the universal set.
Subsets: If A and B are sets such that each element of A is an element of B, then we say that A is a subset of B and write A Í B.
Power Set: The family of all subsets of any set S is called the power set of S. We denote the power set of S by P (S).
Hope you like the above example of Sets.Please leave your comments, if you have any doubts.
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