Theory of Sets

Idea of a set was first introduced in the 19th century by the German mathematician George Cantor (1845-1918), who conceived set as a collection of objects. In late 19th century Frege developed this idea further, but his work did not attract much attention. In 20th century Bertrand Russell rediscovered this idea independently and his work in 1903 led to the monumental work in the foundation of the theory of sets.We often come across such phrases as ' a herd of buffalos'; ' a bunch of bananas'; 'a class of student's; 'the collection of all positive integers'; etc. In these phrases; buffalos, bananas, students, all positive integers are all examples of well defined objects that have been grouped or collected together and viewed as a single object herd, bunch, class, collection. Mathematicians use the word set for a single object. Here our main objective is to provide the basic knowledge of set theory which is useful in solving problems on counting, problems related to combinatories, to study various discrete structures such as graphs, groups and rings.