devotion & mathematics

    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 ⇒ ∞ = ∞. 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 non - termin...

contents : 1. Extended real number system 2. The symbol infinity 3. Properties of infinity THE EXTENDED REAL NUMBER SYSTEM :                                    Basically the real number system not contain + or -  ∞, it  contains all the real numbers lies between for - ∞ and + ∞ i.e.  the real number system R=(- ∞. ∞).                                     The extended real number system is a union of the real number set R and the symbols - ∞ and + ∞ i.e. Extended real system = R ⋃ {- ∞, ∞} = [- ∞, ∞]    In extended real number system,  ∞ is an upper bound   and - ∞ is a lower bound of every subset. Here we see an example to tell the main difference between real and extended real number systems.     Consider an open interval (2, ∞).  The interval (2, ∞) i...