What is zero divided by zero?

Answer

0 / 0 is undefined. However, you can make the case that the answer is "any real number". If a / b = c, then a = b x c. If a = b = 0, then, in the multiplication version of the equation, any real number works as a value of c.

Answer

To be exact, the division operation does not exist! A division is actually a multiplication by another very special number. What we mean when we say "divide A with B" is actually "multiply A with a certain number, lets call it X, that gives 1 when multiplied by B ( i.e. X*B = 1 we usually call X the inverse of B and we refer to it as B^-1 )

So I must remember A / B = A * X

Now if I say B = 0 , and I consider A / B , I am assuming I found a certain number X with the propriety that

X*B = 1

That is

X*0 = 1

On the other hand, we know that for any given number N we have the multiplicative propriety that

N*0 = 0

This is because if you take a number 0 times, you will always have 0 in your hands, regardless of what that number you didn't pick up was. This is unquestionable.

But since this works for any number N, and I assumed there exists a number X that is the inverse of 0, I'm now going to combine the two last stated equations by choosing my number N equal to X ( i.e. N=X ).

So by the inverse propriety we have

1 = N*0

since I chose N to be X, the inverse of 0.

We also have by the multiplicative propriety of the number 0

N*0 = 0

So this leads us to:

1 = N*0 = 0

=> 1 = 0 Which is agreed impossible.

This can only mean that I am wrong when I assume there is an inverse number for 0.

Consequently, whenever I wright down something by the lines of A / 0 ( like 0 / 0 ) I'm actually making no mathematical sense.

Another answer

The question could also be answered by using another technique in maths.
It is agreed that 0/0 is meaningless, but if this is a maths problem that requires an answer, then this would be an alternative way to come to the answer:
Consider Y = 0/X. Now, if one calculates the value of Y when X=1, it is obvious that the answer is zero.
If X = 1/2, the answer is zero.
If X = 1/4, the answer is zero.
If X = 1/100, the answer is zero.
If X = 1/10000000000000, the answer is still zero.

So, as the value of X gets smaller, the value of Y tends to stay zero.
On this argument, I would say that when there is a practical reason to give an answer to this question (for example in engineering or quantum physics), I would suggest that the answer is Zero.

The nifty thing is that you can check this answer:

> Y = 0/X

> Y*X = 0

> When X and Y are zero, it is correct to say that 0*0=0

Answer (joke)

A segfault.

Answer: hello...u don't need to be einstine....do u have a calculator....wats with all the calculations!?! lol!

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