Dividing Zero By Zero

@ehBeth,

ehBeth, Good suggestion, but my brain has retired from "work," and my only pleasures now are travel, photography, friends, family, and a2k. Laughing

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@cicerone imposter,

cicerone imposter wrote:

guigus wrote:
Quote:
nothing multiplied by zero equals one.

Show us how this works in the "real" world? Zero (or nothing) times zero (or nothing) can never equal 1.

No oranges times no oranges will never equal 1. Where did that one orange appear from? You have a very good imagination.

Are you playing dumb? Please pay attention:

1. No number multiplied by zero equals one, since any number multiplied by zero equals zero.
2. Zero multiplied by zero does not equal one, since no number multiplied by zero equals one.

This already shows that zero is a number, which is different from the absence of any number. However, what multiplied by zero equals one? The answer is: nothing. Not only no number, but also nothing else, that is, nothing at all. So nothing multiplied by zero equals one, hence the difference between zero and nothing:

1. Nothing multiplied by zero equals one, since anything -- multipliable by zero -- multiplied by zero equals zero.
2. Zero multiplied by zero does not equal one, since nothing multiplied by zero equals one.

Zero being different from nothing would only make it nonzero if it were identical to nothing, which it is not.

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@cicerone imposter,

cicerone imposter wrote:

That's probably why I'm not privy to understanding how zero can mean more than how I understand it. I've never been exposed to the "sub-world of mathematics."

My career was in accounting and administration of several companies, and zero always meant it had no value, and it never translated into "1."

Zero does not "translate into one," and I never said so.

And zero does not mean more than how you understand it, it means less: it is just quantitative nothingness, rather than absolute nothingness, which is how you "understand it."

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FWIW, my understanding:

When you draw a number line, the actual location of zero in reality doesn't exist no matter how fine you make the resolution of the drawing. There is always a quantity of some sort as you approach from positive numbers to negative numbers - even an infinitesimal fraction, either positive or negative.

However, for the sake of illustrating on a number line, we can point to the approximate area where zero theoretically can be located. That is not relevant to an actual useful place in the physical world, as zero is nothingness and has no property in the real world. It is the absence of anything - non-quantifiable.

And, of course, zero has no physical characteristic - no useful division by zero exists without equaling zero. So, I've no idea why people wrote about multiplying by zero can ever give you anything but zero.

-5....-4....-3....-2....-1....theoretica'lly nuttin ....+1....+2....+3....+4....+5

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@guigus,

It doesn't mean less; it means non-existent. The topic of this thread is "Dividing Zero By Zero.

Ragman, You and I are on the same page.

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@cicerone imposter,

cicerone imposter wrote:

It doesn't mean less; it means non-existent. The topic of this thread is "Dividing Zero By Zero.

Ragman, You and I are on the same page.

Please address my post http://able2know.org/topic/161595-7#post-4463916. Otherwise, it would be very difficult for us to make any progress.

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@Ragman,

Ragman wrote:

FWIW, my understanding:

When you draw a number line, the actual location of zero in reality doesn't exist no matter how fine you make the resolution of the drawing. There is always a quantity of some sort as you approach from positive numbers to negative numbers - even an infinitesimal fraction, either positive or negative.

In other words: zero is the absence of any quantity, it is quantitative nothingness, which is precisely what I am saying.

Ragman wrote:

However, for the sake of illustrating on a number line, we can point to the approximate area where zero theoretically can be located. That is not relevant to an actual useful place in the physical world, as zero is nothingness and has no property in the real world. It is the absence of anything - non-quantifiable.

Zero has no place in the physical world, since it is not an object but a number, and I never said otherwise. But it is not the absence of anything: it is rather the absence of any quantity, which you keep failing to grasp.

Ragman wrote:

And, of course, zero has no physical characteristic - no useful division by zero exists without equaling zero.

This is a great mess: no number has physical existence, even if its multiplication by another number has a nonzero result. What exists physically are the objects of which the quantity numbers refer to.

Ragman wrote:

So, I've no idea why people wrote about multiplying by zero can ever give you anything but zero.

Who wrote that? Certainly I didn't.

Ragman wrote:

-5....-4....-3....-2....-1....theoretica'lly nuttin ....+1....+2....+3....+4....+5

You are misunderstanding both zero and me: zero has no value, it represents no quantity, but it is not identical to absolute nothingness, precisely because it has no qualitative dimension, only a quantitative one, as the following shows:

1. There is nothing that multiplied by zero equals one: nothing multiplied by zero equals one.

2. Anything multipliable by zero -- any number, including zero -- multiplied by zero does not equal one: zero multiplied by zero does not equal one.

Nothing multiplied by zero equals one, while zero multiplied by zero does not equal one, so nothing must be different from zero, since they behave differently when multiplied by zero.

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To make it even clearer:

Is there any number that multiplied by zero equals one? Of course not: no number multiplied by zero equals one. So zero -- which is a number -- multiplied by zero does not equal one. Besides, nothing can be multiplied by zero resulting in one, since only numbers can be multiplied at all.

Nothing can be multiplied by zero resulting in one, but zero cannot be multiplied by zero resulting in one. Then, zero behaves differently from nothing, simply because nothing is not a number, while zero is.

What makes zero a number? It is its being the absence of only a quantity, while nothing is the absence of a quantity and a quality.

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@guigus,

I enjoy reading your contradictions in one post; it belongs on the laffer curve.

Let's see: o oranges divided by zero oranges = 1. Yup, got that!
The poof man lives!

1 Reply

@cicerone imposter,

cicerone imposter wrote:

I enjoy reading your contradictions in one post; it belongs on the laffer curve.

Let's see: o oranges divided by zero oranges = 1. Yup, got that!
The poof man lives!

What relation does this have to my previous post (not that I have much hope of getting a decent answer)?

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@guigus,

Zero has to have an application on anything that can be counted before it arrives at zero. Zero of nothing is nothing. Dividing nothing by nothing still equals zero.

What is that "something" you are counting to produce the `1'?

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One object must be different from another object, or they would no longer be two different objects, but rather one identical object. However, when we consider their quantities, they are precisely the same -- one. Such is the nature of numbers: one is always one, there are no different "ones."

We can regard an object as absent, so its absence is the absence of its qualities, but when we consider the absence of its quantity, we must forget about any qualities. This quantitative nothingness is the number zero: it is never the absence of any qualities, but rather the absence of any quantity. Zero chairs is identical to zero cows, there are no different "zeroes." On the other hand, no cows is different from no chairs: their nothingness inherits their qualities.

1 Reply

@cicerone imposter,

cicerone imposter wrote:

Zero has to have an application on anything that can be counted before it arrives at zero. Zero of nothing is nothing. Dividing nothing by nothing still equals zero.

Sorry, but nothing is not a number, so it cannot participate in division or any other mathematical operation -- you are confusing nothing with zero.

cicerone imposter wrote:

What is that "something" you are counting to produce the `1'?

Sorry, but you must explain yourself better, the above does not make sense to me.

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@guigus,

So dividing zero chairs by zero cows is still zero. We're talking about both quantity and quality. It doesn't matter what objects you place in front of or back of a zero; it still results in a zero.

Your attempts to use different objects to divide is not logical when both are zero.

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@cicerone imposter,

cicerone imposter wrote:

What is that "something" you are counting to produce the `1'?

Does this refer to the sentence "nothing multiplied by zero equals one"? If so, then you are just confusing nothing with something.

My sentence asserts that nothing can be multiplied by zero to give us one, either because it is not a number, hence cannot be multiplied at all, or because, despite being a number, when multiplied by zero gives us only zero -- never one.

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@cicerone imposter,

cicerone imposter wrote:

So dividing zero chairs by zero cows is still zero. We're talking about both quantity and quality. It doesn't matter what objects you place in front of or back of a zero; it still results in a zero.

Dividing zero by zero gives you any number -- which is why mathematicians have forbidden dividing by zero -- and mathematics has no representation of a cow or of a chair to place "in front" or in the "back" of any number: in mathematics there are only numbers and the operations between them.

cicerone imposter wrote:

Your attempts to use different objects to divide is not logical when both are zero.

It is you that are putting different objects "in front" and in the "back" of numbers, not me: I am saying precisely that all numbers, including zero, disregard quality. Numbers reduce objects to their quantity, so the only difference left is the difference between different quantities: in mathematics, three cows are identical to three chairs, just because mathematics disregards cows and chairs alike to consider only their number, which, in this case, is one and the same: three. That's the difference between zero and nothing: zero -- as any other number -- disregards quality, while nothing does not.

1 Reply

@guigus,

You're the one who brought chairs and cows into this discussion.

You wrote:

Quote:

We can regard an object as absent, so its absence is the absence of its qualities, but when we consider the absence of its quantity, we must forget about any qualities. This quantitative nothingness is the number zero: it is never the absence of any qualities, but rather the absence of any quantity. Zero chairs is identical to zero cows, there are no different "zeroes." On the other hand, no cows is different from no chairs: their nothingness inherits their qualities.

[/b]

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@cicerone imposter,

cicerone imposter wrote:

You're the one who brought chairs and cows into this discussion.

You wrote:
Quote:
We can regard an object as absent, so its absence is the absence of its qualities, but when we consider the absence of its quantity, we must forget about any qualities. This quantitative nothingness is the number zero: it is never the absence of any qualities, but rather the absence of any quantity. Zero chairs is identical to zero cows, there are no different "zeroes." On the other hand, no cows is different from no chairs: their nothingness inherits their qualities.
[/b]

First of all, I'm glad you are addressing my text. What the above means is that there is no place in mathematics for chairs or cows: zero disregards chairs and cows alike, so it doesn't matter what you are talking about -- zero chairs is identical to zero cows, because mathematics reduces chairs and cows to their quantity, which is always identical for the same number of chairs, cows, dollars, or whatever.

On the other hand, no cow -- instead of zero cows -- regards quality: it is the absence of a cow, not of anything else. That's the difference between the idea of nothingness and the number zero: the former concerns quality, the latter does not.

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@guigus,

But, but, but....quality is a whole different issue from zero divided by zero. You already said it "it doesn't make any difference" which tells me there is nothing qualitative. Therefore, there is nothing quantitative or qualitative. Nothing divided by nothing is always zero. There is only zero to represent what you are looking at. No value, no quality, and no quantity.

1 Reply

@cicerone imposter,

cicerone imposter wrote:

But, but, but....quality is a whole different issue from zero divided by zero. You already said it "it doesn't make any difference" which tells me there is nothing qualitative. Therefore, there is nothing quantitative or qualitative. Nothing divided by nothing is always zero. There is only zero to represent what you are looking at. No value, no quality, and no quantity.

Numbers must concern quantity and cannot concern quality, by definition. And zero is no exception, so it means "no quantity" but not "no quality." Which doesn't prevent you from concluding that, if there is no quantity, then there must be no quality as well, but this is you thinking, not zero talking: religious people may well believe in quality without quantity, and many religious people are mathematicians. Numbers don't give a damn about such beliefs: quality simply does not belong to their meaning: numbers, including zero, simply disregard quality. The concept of nothingness, on the contrary, does not have that limitation: it regards both quantity and quality, which becomes clear if we try to answer this question:

What multiplied by zero equals one?

Of which a valid answer is "nothing," but never "zero." Why? Because the number zero is only a quantity -- the null quantity -- that multiplied by that same quantity gives us itself again rather than one. Answering "zero" to the question above is committing a mathematical error, while responding "nothing" is mathematically correct. Hence, nothing and zero are different.

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Dividing Zero By Zero

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