Small set vs Finite set : Real Analysis

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 that  ℛ is not a 

small set. 

                For that  take an empty small bottle. Now what is bottle holding. Air. In that small bottle 

there are infinitely many air particles. We can not see as well as we can not count that air 

particles. Even though the bottle is small , that bottle containing infinite air particles. 

       In the similar manner even though the real  line ℛ containing  infinite numbers, ℛ  is a small 

set.

      In the similar manner small and finite sets are differ.  

                                                    ***** 

 

 * infinite series

 * what is a metric?

 * What is a pseudo metric?

 #small #set #vs #finite #set  #: 

#real #analysis