(I have to much time on my hands)

Currently, n divided by zero(0) is undefined.

Why? What are your thoughts on this, and any possible theories for a definition for n/0 ?

********My Theories********
Code:

Example 1.1:
          1          |          2          |          3
5 * 6 = 30           |      30 / 5 = 6     |      30 / 6 = 5
10 * 3 = 30          |      30 / 10 = 3    |      30 / 3 = 10
                        
Example 1.2:
          1          |          2          |          3
0 * 5 = 0            |      0 / 0 = ?      |      0 / 5 = ?
0 * 10 = 0           |      0 / 0 = ?      |      0 / 10 = ?


     In example 1.1, If two numbers are multiplied together, their
product divided by one of the numbers should only equal
the other number.  This is because the only way to reach the
product with the given number is to multiply it(or add it to itself)
x amount of times, where x is the other number.
     
     Of course, the same should apply to division by zero, and if
you think about, it indeed does in column three of example 1.2.    
Zero divided by zero, however, could be any given number,
because any number multiplied by zero equals zero.

     This is where one of the problems of defining division by zero
arises.  In one case, where zero is divided by a non-zero number,
It follows basic rules, but in the other, zero divided by zero, it is
impossible to tell what it should be.  What could you put in there
to make the statement always correct?

Now for the next part:


Example 2.1:
2 / 0 = ?
10 / 0 = ?


     The same as the zero divided by zero case, except with a new
twist: zero multiplied by anything will never equal a number
other than zero, but now we're trying to divide a number by
another number that would never multiply into it?!  That the
denominator should multiply into the numerator is essential in the
multiplication/division relationships!

     Since it is impossible to achieve an answer through the former
methods of thought, I propose a new one.  In division, you
basically take the numerator and put equal amounts of it into a
number of groups equal to the denominator and finding out the
number in any given group.


Example 3.1:
10 put equally into 5 groups = 2 in any group
30 put equally into 3 groups = 10 in any group
     

     Following this method, (this could be a bit confusing: )putting
a number into zero groups should equal zero in any of the group
(The confusing bit: even though there are no groups..), so: 


Example 3.2:
10 put equally into 0 groups = 0 in any group
30 put equally into 0 groups = 0 in any group


     Problem: what happened to the initial amount?  If this were
done with energy, which can be neither created nor destroyed,
this would be impossible.  So now I propose, in conjunction with
this, that a special convention be applied to this case.  

     A convention such as I mentioned has already been entered
into algebraic math: A negative number has no real square
root, but this has been solved by putting an i on the outside
of the square in this way:


Example 4.1:
i^0 =  1
i^1 =  i
i^2 = -1
i^3 = -i
i^4 =  1
i^5 =  i
i^6 = -1
i^7 = -i
etc.

Example 4.2:
root -16 = root (16 * i^2) = i(root 16) = 4i
root -49 = root (49 * i^2) = i(root 49) = 7i

2i = 2i
2i^2 = -2
2i^3 = 2(-i)
2i^4 = 2


     Use of a convention such as this would definitely help in the
continuance of a problem without a stall at the point of division
by zero.  How to implement this convention presents yet another
problem, but which I, at this time, unfortunately have no idea
how to do.
If you have gotten this far, thank you for your time, if you understood and could follow me, even better. Either way, all comments, thoughts, or theories would be much appreciated. Again, thanks for your time and input.