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# What is a set?

A set is a collection of elements usually of the same kind. Eachset can be denoted by a capital letter. A set may be defined bylisting the members or describing the members. A… set is said to befinite when all its members can be listed. The above is an intuitive definition which seemed sufficient forseveral years but then contradictions such as Russel's paradox werepointed out, so a great deal of work had to be done to developaxioms that could define sets without allowing any paradoxes. Theseaxioms require considerable mathematical sophistication tounderstand and often are the basis for a senior level college math A set is a collection of items. For example the set of furniture in a bedroom might be {bed, besidecupboard, dressing table, wardrobe, chair}; this is an example of afinite set as there are a finite number of elements in the set. Another example is the counting numbers {1, 2, 3, ...}; this is anexample of an infinite set as there is no end to the members of theset and it is impossible to list everyone of them. A countable set is a set that can have each of its members put intorelation with one of the counting numbers. Both the above examplesets are countable. (MORE)