WHY A NUMBER DIVIDE BY ZERO IS UNDEFINE ? or why X/0=UNDEFINE ?

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 Hi I am your teacher Ansh again... hope you like this one also .Subscribe us if you like this one 

So lets start..

WHAT IS DIVISION ?

To understand todays topic we need to understand the basic ,What is division?  In simple layman's term 
division is to subtract a number (say x) repeatedly  from a number (say y) but in a way that nothing left(or the remainder is equal to zero hence the number of time x is repeated is the value of our division

to understand it properly lets take an example:

 Say we have to division like 15/3. hence from above discussion we can say that 

15-3-3-3-3-3=0  Here 3 is repeated 5 times so the answer of division is 5

or 100/20

100-20-20-20-20-20=0 Here 20 is repeated 5 times so the answer for this question is 5

SO WHAT IS X/0 THEN?

To answer this ..let us say we have an equation 1/0.  Hmm.. lets try to use our basic  definition of division so 
1/0=1-0-0-0-0-..... 
do you see, it keeps going on .It goes on to ∞. now from this  we can conclude that 1/0=∞  but is that it  we need something powerful hmm.. lets try to divide again but not directly with zero but using "tends to zero "  like  shown in figure 


do you see  a pattern here . as we moving closer closer to 0  the value start increasing  so from this  isn't is right for us to conclude that if the  denominator is equal to zero then the value is equal to ∞ . 

Now don't you think that we have find the value of 1/0 from two different ways and from both ways we get the value of 1/0=∞  ,So the value should be 1/0=∞ ... before moving to this conclusion  we have one another way to solve this division using "tends to zero "  .lets use that one also  . Now as shown in fig.
 

Wait what was that , now in this case we are still approaching to zero but the result is different .Now if we keep going , the result is not in ∞ but in -∞ .Isn't it strange that same division gives 2 different solution which are not only unique but also completely opposite. So this gives contradiction to our previous conclusion . But wait not only that  let us change the numerator a bit so instead of 1/0 we can write it as 2/0  So, 2/0=2-0-0-0-0-.....  same result is given in both case of basic division and in tends to zero division . 
Now if we assume that 1/0=∞ and 2/0=∞ then we can say that 1/0=2/0 or 1=2 But we all know that it  is impossible

So from this we can conclude that neither of the answer is satisfied 
hence it is not undefine because we want to write it .. It is undefine because it is undefinable 

Hence from this we can say that     X/0=UNDEFINE    not  ∞

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