What's the value of 0/0 ?

Do you know what's the value of 0/0 ?
Most books just don't care about it. Also many teachers are not interested to touch anything like this. Students are fearing to see this, especially while they are doing some calculations on the exam paper!
Anyway, it is good to be aware of 0/0. I continue this article assuming you know basic addition, multiplication etc.
One question: What's the value of 10/2 ?
It's 10/2 = 5. Is it?
We got the answer as 5. Is that mean 5*2 =10 ?. For example, if you have money Rs.10 and distributed to your two friends equally. Then your friends get 10/2 = Rs.5 each.
From the above example, we can generalize that if a fraction exist in the form x/y=z , then z*y =x.
please note the above line. I will tell you more about that line!
Then the question is if you divide your Rs.x to y people equally, each will get  Rs.z. Then what is z?
The answer z is a number which satisfies z*y=x. In the above example, you put different values for z such that, z*2 =10. Then z is the amount in your each friend's hand. Here 5, the only 5 satisfies the equation when it put to z. Thus each of your friend get exactly Rs.5.
Then consider the case of 0/0 . Like the previous example, if 0 is divided to 0 people, how many rupees each of your friend get? If  the answer of this question is z, we can write z*0 = 0. Put some values for z in order to satisfy the equation. All values of z which satisfies the above equation are the solution. We know that multiplication of any value with 0 is 0. So z can take any values to satisfy the equation.
If the solution of z is written in a page, your page may not be sufficient to include all solutions of the equation because solution is 'any value'. More mathematically,
z = -infinity.......................0.......................+infinity
So, 0/0 = any value
It seems very interesting on the first sight. You have nothing, and you are dividing that to nobody. Then the amount in the nobody's hands may be millions, trillions or anything. If you think, this is like a magic to generate millions from nothing, you are absolutely wrong. Think about it.
Let's go for an example to describe what's actually I am trying express. To understand this example, you should aware of a great law named Ohm's law in Electricity (The circuit shown below is stolen from Wikipedia). If you don't know anything about Ohm's low, you must make yourself aware of that before going to continue.

According to Ohms law (refer picture), R is V/I.

R=V/I

If V=10V and I=2A, then R = 10/2 = 5 ohm. In the above picture, if Voltage V=0, Current I will also be zero (without voltage there will no current). Then R = V/I =0/0.
According to our previous result 0/0 can be 'any value'. So R = 0/0 simply means R can take any value. R can be anything.
R*0 =0 can be treated like this: R is the values that exists when V=0 and I=0.
If you put a resistor in your pocket, the applied voltage V = 0 and hence current I = 0. So you can put Resistances of any value in your pocket. Think about the world of 0/0 = a fixed value. For example, take the fixed value 0/0 = 100. Then Resistance R =100ohm is the only value that can put into your pocket and others can't!
Seems funny? but it is fact.