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Small set vs Finite set : Real Analysis

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Small Set Vs Finite Set :          In mathematics, from so many years there is a confusion to few members who are interested  in  learning mathematics about small and and finite set. Most of people thought that small set and  finite set  are same. Basically small  and finite sets are not same.           We know a set is called finite set if the length of set is finite. Then  what about small set. In  mathematics, a small set does not have one universally fixed meaning. But with a small example,  we can found that what is a small set and how it differs from finite set.                   Example :                Consider the real line ℛ. We all know that  ℛ is an infinite set. Hence it is clear that  ℛ  is not a finite  set.  Even though ℛ is not a finite set , we can not conclude ...