Zero divided by zero revisited

[alan1000]

A recent post on this question quickly descended into levity. However, it is a genuine philosophical problem in arithmetic, so let's try again, shall we?

There are four possible answers:

0/0 = 0 (based on the intuitive supposition that only zero quantities are involved, so there cannot be a non-zero answer).

0/0 = 1 (based on the supposition that n/n=1)

0/0 = infinity (assuming 0 = h)

0/0 = Ø (the division fails because the null set is indivisible)

All four positions can be supported by respectable mathematical arguments. What's your preference?

[nemos]

Nothing divided by nothing, sounds philosophical to you, not to me. Or can you somehow justify that 0 is not a nothing?
No one does anything with 0, because there is no need. It is nothing more than an empty mind-bending out of boredom that has no practical application. About the same as trying to prove that 2*2=5.

[Age]

'you' can NOT divide by zero.

[attofishpi]

A recent post on this question quickly descended into levity. However, it is a genuine philosophical problem in arithmetic, so let's try again, shall we?

There are four possible answers:

0/0 = 0 (based on the intuitive supposition that only zero quantities are involved, so there cannot be a non-zero answer).

0/0 = 1 (based on the supposition that n/n=1)

0/0 = infinity (assuming 0 = h)

0/0 = Ø (the division fails because the null set is indivisible)

All four positions can be supported by respectable mathematical arguments. What's your preference?

I'm gonna go with A: 0/0 = 0 (nothing all the way - kind of agree with nemos)

[Skepdick]

All four positions can be supported by respectable mathematical arguments. What's your preference?

All of them.

Depending on the context.
Depending on what the / operator means; and depending on what 0/0 is supposed to represent/denote.

Manipulating and evaluating mathematical objects/expressions is the epitome of a designing computer algebras/symbolic computations.

https://en.wikipedia.org/wiki/Computer_algebra

[Dontaskme]

What's your preference?

There isn't one.

One can only be divided by itself, which always sums to zero, where no division exists.

[alan1000]

Nothing divided by nothing, sounds philosophical to you, not to me. Or can you somehow justify that 0 is not a nothing?
No one does anything with 0, because there is no need. It is nothing more than an empty mind-bending out of boredom that has no practical application. About the same as trying to prove that 2*2=5.

I'm guessing you have the usual familiarity with arithmetic, but not with mathematical philosophy? Set theory? Number theory?

[alan1000]

'you' can NOT divide by zero.

You forgot to provide supporting arguments, as required by the rules of this forum. If you can provide such arguments, I will reply.

[alan1000]

Nothing divided by nothing, sounds philosophical to you, not to me. Or can you somehow justify that 0 is not a nothing?
No one does anything with 0, because there is no need. It is nothing more than an empty mind-bending out of boredom that has no practical application. About the same as trying to prove that 2*2=5.

I'm sorry, but I have no idea what this reply is asserting, in the context of mathematical philosophy.

[alan1000]

A recent post on this question quickly descended into levity. However, it is a genuine philosophical problem in arithmetic, so let's try again, shall we?

There are four possible answers:

0/0 = 0 (based on the intuitive supposition that only zero quantities are involved, so there cannot be a non-zero answer).

0/0 = 1 (based on the supposition that n/n=1)

0/0 = infinity (assuming 0 = h)

0/0 = Ø (the division fails because the null set is indivisible)

All four positions can be supported by respectable mathematical arguments. What's your preference?

I'm gonna go with A: 0/0 = 0 (nothing all the way - kind of agree with nemos)

Supporting arguments?

[alan1000]

All four positions can be supported by respectable mathematical arguments. What's your preference?

All of them.

Depending on the context.
Depending on what the / operator means; and depending on what 0/0 is supposed to represent/denote.

Manipulating and evaluating mathematical objects/expressions is the epitome of a designing computer algebras/symbolic computations.

https://en.wikipedia.org/wiki/Computer_algebra

This is at least a philosophically intelligible reply. Skepdick is right; all of the answers are correct, on condition that one specifies the appropriate mathematical context. (I deliberately say 'one' rather than 'you', because one poster seemed to take exception to the second-person pronoun).

But is there any reason to prefer one answer over the others? Because it is obvious that, in any philosophical discourse, where apparently-conclusive arguments lead to contradictory outcomes, the enquiry must have taken a wrong turn somewhere. Is there any over-reaching argument to favour one solution over the others?

[Age]

'you' can NOT divide by zero.

You forgot to provide supporting arguments, as required by the rules of this forum. If you can provide such arguments, I will reply.

One only has to look at a computer or calculator to come to see and understand that 'you' can NOT divide by zero.

However, and of course, if 'you' CAN divide by zero, then, please, explain HOW, EXACTLY, and what answer 'you' get/got, EXACTLY.

Now,
P1. For EVERY one else and for EVERY computer/calculator 'they' can NOT divide by zero.
P2. No one has YET shown HOW 'they' CAN divide by zero.
Therefore, until 'you', or someone else, can SHOW, EXACTLY, how 'you/they' CAN divide by zero, then 'this argument' will suffice.

[Flannel Jesus]

However, it is a genuine philosophical problem in arithmetic, so let's try again, shall we?

Is it? Do you have any resources to show that mathematicians in general agree that this is a genuine problem?

[Age]

All four positions can be supported by respectable mathematical arguments. What's your preference?

All of them.

Depending on the context.
Depending on what the / operator means; and depending on what 0/0 is supposed to represent/denote.

Manipulating and evaluating mathematical objects/expressions is the epitome of a designing computer algebras/symbolic computations.

https://en.wikipedia.org/wiki/Computer_algebra

This is at least a philosophically intelligible reply. Skepdick is right; all of the answers are correct, on condition that one specifies the appropriate mathematical context. (I deliberately say 'one' rather than 'you', because one poster seemed to take exception to the second-person pronoun).

But is there any reason to prefer one answer over the others? Because it is obvious that, in any philosophical discourse, where apparently-conclusive arguments lead to contradictory outcomes, the enquiry must have taken a wrong turn somewhere. Is there any over-reaching argument to favour one solution over the others?

But if 'you' can NOT divide by zero, which, so far, 'you' can NOT, (as 'you' have NOT YET provided ANY supporting sound AND valid argument of HOW 'you' could), then there is NO so-called 'over-reaching argument', which favors one 'solution' over 'other ones'. As there OBVIOUSLY IS NO 'solution' AT ALL.

[alan1000]

'you' can NOT divide by zero.

You forgot to provide supporting arguments, as required by the rules of this forum. If you can provide such arguments, I will reply.

One only has to look at a computer or calculator to come to see and understand that 'you' can NOT divide by zero.

However, and of course, if 'you' CAN divide by zero, then, please, explain HOW, EXACTLY, and what answer 'you' get/got, EXACTLY.

Now,
P1. For EVERY one else and for EVERY computer/calculator 'they' can NOT divide by zero.
P2. No one has YET shown HOW 'they' CAN divide by zero.
Therefore, until 'you', or someone else, can SHOW, EXACTLY, how 'you/they' CAN divide by zero, then 'this argument' will suffice.

I'm sorry, Age, but I can't write a thousand-word essay in this forum to explain mathematical philosophy to you. You will need to research it for yourself.

But I would ask you: you obviously believe that 0/0=1 is fallacious, and thus, n/n=1 is false when applied to the number 0. What are your arguments, exactly?