Zero divided by zero revisited
Zero divided by zero revisited
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?
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?
Re: Zero divided by zero revisited
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.
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.
Re: Zero divided by zero revisited
'you' can NOT divide by zero.
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Re: Zero divided by zero revisited
I'm gonna go with A: 0/0 = 0 (nothing all the way - kind of agree with nemos)alan1000 wrote: ↑Sat Dec 23, 2023 1:10 pm 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?
Re: Zero divided by zero revisited
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
Re: Zero divided by zero revisited
I'm guessing you have the usual familiarity with arithmetic, but not with mathematical philosophy? Set theory? Number theory?nemos wrote: ↑Sat Dec 23, 2023 4:05 pm 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.
Re: Zero divided by zero revisited
I'm sorry, but I have no idea what this reply is asserting, in the context of mathematical philosophy.nemos wrote: ↑Sat Dec 23, 2023 4:05 pm 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.
Re: Zero divided by zero revisited
Supporting arguments?attofishpi wrote: ↑Sun Dec 24, 2023 2:40 amI'm gonna go with A: 0/0 = 0 (nothing all the way - kind of agree with nemos)alan1000 wrote: ↑Sat Dec 23, 2023 1:10 pm 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?
Re: Zero divided by zero revisited
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).Skepdick wrote: ↑Sun Dec 24, 2023 8:40 amAll 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
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?
Re: Zero divided by zero revisited
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.
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Re: Zero divided by zero revisited
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 wrote: ↑Thu Dec 28, 2023 12:28 pmThis 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).Skepdick wrote: ↑Sun Dec 24, 2023 8:40 amAll 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
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?
Re: Zero divided by zero revisited
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.Age wrote: ↑Thu Dec 28, 2023 12:38 pmOne 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.
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?