devotion & mathematics

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 ...

    what heppened when   ∞/∞ =1?  " Infinity " , In my earlier post , we have discussed about infinity and its properties. Come to our question " what happened when ∞ / ∞ = 1 ? " Assume   ∞/∞ = 1 that implies ∞ = ∞. Let the ∞ in the L.H.S. is the number of water drops in a riverand the ∞ in the R.H.S. is the  number of  water drops in a sea. It is impossible to count the number of water drops in a sea as  well as in the river.  That why we  consider both having infinite water drops. Now as our  assumption  if ∞ = ∞ then the  number of water drops in a river must equal to the number of  water  drops in a sea it results  the river  and sea must be of equal in size.  Is it true? No. Hence ∞  ≠ ∞ i.e. ∞/∞ ≠ 1. First of all this question may arise only if ∞ is a number.  Now my question " Is ∞ a mumber ? "  Answer is  ∞ is not a number. It is a symbolic representation of n...