0 divided 0 = ?

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Zero may or may not be a natural number, but it is a whole, real number and integer.

You can't define 1-1 without it.
 
Beer w/Straw said:
Zero may or may not be a natural number, but it is a whole, real number and integer.

You can't define 1-1 without it.
Click to expand...

In layman's terms could we say that while zero is a real number it can only be a non-functional result. As zero has no properties (in and of itself) it cannot function as a causality. It is non-perturbative and has no effect as a causal function, i.e. while 3-3 = 0, 3*0 = 0, but 3/0 = 3
Thus 0/0 = 0

Am I getting the gist of this?
 
No -- zero is a number -- but division is not an operation which is guaranteed to work for all elements of a ring or field.

Addition, Negation, Multiplication, and Distributivity are guaranteed. Division by x only works if you can solve the equation $$ x y = 1$$, because then division by x would be the same thing as multiplication by y.
 
rpenner said:
No -- zero is a number -- but division is not an operation which is guaranteed to work for all elements of a ring or field.

Addition, Negation, Multiplication, and Distributivity are guaranteed. Division by x only works if you can solve the equation $$ x y = 1$$, because then division by x would be the same thing as multiplication by y.
Click to expand...

I am not following this.

OK, 0 is a number. The rest seems odd.
 
Oh, I think I see what you were saying RPenner. You generalized division in that 1/2 is not a natural number. Yet, neither is 1/0.

It depends on your universe.

OK, I narrowed on the previous post of real number. So, your post reveals 2 reasons why division may not work. 1) The result is valid/functional but not in the range. 2) The result is not functional.

I will have to agree.
 
Mathematics, I thought, was a language with which to interpret reality.

On that premise, I have zero apples on my desk. How can I then speak of dividing that which is not ?

I have zero islands in the Carrabian, too, so I can't sub-divide anything in the Carrabian.

Therefore, on that 1st, most basic premise, 0/0 is non-sense.
 
Not all all. If you have 3 sons and 0 Caribbean islands, when you die intestate each of your sons inherits $$\frac{0}{3} = 0$$ Caribbean islands.

Now if you had zero sons and 16 Caribbean islands, since you can't divide by zero, the state takes everything.
 
rpenner said:
Not all all. If you have 3 sons and 0 Caribbean islands, when you die intestate each of your sons inherits $$\frac{0}{3} = 0$$ Caribbean islands.

Now if you had zero sons and 16 Caribbean islands, since you can't divide by zero, the state takes everything.
Click to expand...

I appreciate your answer, however, could you re-state it without the mathematical equation ?
 
rpenner said:
No -- zero is a number -- but division is not an operation which is guaranteed to work for all elements of a ring or field.

Addition, Negation, Multiplication, and Distributivity are guaranteed. Division by x only works if you can solve the equation $$ x y = 1$$, because then division by x would be the same thing as multiplication by y.
Click to expand...

You say, "no", but where specifically does my logic fail?

a) x-x = 0 (result as a real number) True?

b) x*0 = 0 (non functional factor) True?

c) x/0 = x (non-functional divisor) True?

If x = 0, then x/0 = 0 (non-perturbative function) True?
 
Sifur said:
Hey folks, I'm new so hopefully this discussion hasn't came up recently.

Is 0/0= undefined because it has infinite possibilities?
Click to expand...
I don’t think the reason why it is undefined is because it has an infinite possibility of values or answers.
Zero by itself is either a placeholder or has no value so when you perform 0/0 the reason in my opinion that it is undefined is because zero has no absolute value, so it results in undefined.
 
Lakon said:
I appreciate your answer, however, could you re-state it without the mathematical equation ?
Click to expand...

Try this.
In John's Will he stated that each of his three sons should have an equal share in his Caribbean Islands.
However, before he died, he lost all the Islands in a poker game.
"Zero Islands divided by three is zero islands each" said the lawyer at the reading of the will.
"Well, at least that's better than nothing" said one of them.
 
There is an unlimited amount of nothing contained within nothing. The answer is indeterminate by the virtue of the absence of limit within nothingness.
 
Captain Kremmen said:
Try this.
In John's Will he stated that each of his three sons should have an equal share in his Caribbean Islands.
However, before he died, he lost all the Islands in a poker game.
"Zero Islands divided by three is zero islands each" said the lawyer at the reading of the will.
"Well, at least that's better than nothing" said one of them.
Click to expand...

In the real world, however, the lawyer would have said;

"Islands are gone. No more islands. Nothing to divide"

As it happens, I have been involved in my past vocation as a 'workout specialist' for major defaulting corporations, etc.

When I appoint a bankruptcy trustee in the case of individuals, or a liquidator in the case of a corporation, and that trustee / liquidator comes to the conclusion that, after having liquidated the assets, there is ZERO dollars left in the defaulters account, he does not tell the creditors "right, now we will divide that by (number of creditors) - he tells them "no assets to be disbursed".

THAT'S the real world, and something similar would have applied to Johns ZERO assets.

But, this introduces unecessary complexity and some wiggle room for word play.

Let's take it back to my original proposition, which loses nothing of the above, and keeps it clean.

I have no (ZERO) apples on my desk. How can I then speak of dividing that which is not ?
 
One is an odd number so no, zero divided by zero is not even. However during my mathematical travels I have discovered that any number multiplied by two gives an even number. I discovered this trying to solve 0103050709, which I have since discovered has no solution. :)
 
Oh you be quiet! The graph looks as follows (the zero's are simply to make up the spaces but the x's are the values):

900000000x
8000000000
7000000x00
6000000000
50000x0000
4000000000
300x000000
2000000000
1x00000000
00x0x0x0x0
0123456789

...and it is without solution. I discovered this using a program written to discover the relationship between ANY numbers (posted in the compter section). SO what have you got to say about that? :p
 
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