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Understanding / by Zero


conway

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John

 

Please lets drop the rude posting here? I will listen to you. But you need to stop claiming I have dunning kruger issues. The very fact that I have admitted my ability to be wrong, proves this is not the case. You however have yet to admit that ability.

I'm always happy to admit that I'm wrong, when someone shows that is the case.

You have not.

Now, why do you keep claiming things that are obviously not true?

 

Specifically,, so far, you have been wrong in saying;

"If then b=0, then I can say anything / 0 is the thing itself."

You said "If I tell you I have a dog or a poodle.....in neither case does my dog disappear, or become undefined." but nobody ever claimed that the dog was undefined- so it's a strawman.

then there was

"If I hold 5 apples and divide them by zero I still hold 5 apples

If I hold 5 apples and multiply them by zero I still hold 5 apples."

which is begging the question.

Also, in spite of repeated asking, you have yet to answer this "What would you do to divide 5 apples by zero?" in respect of this

If I hold 5 apples and divide them by zero I still hold 5 apples"

So at best you have dreamed up an inconsistent, and therefore unhelpful variation on a theme of maths that lets you "divide by zero" because it arbitrarily changes what the words mean.

Do you feel that's a worthy achievement?

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Bignose

 

If you would read the previously posted axiom that might clear things up.

 

Strange

 

I did not bring it up, another poster did. In any case.....

My apologies if you did not say that zero apples means nothing. I must have crossed this information over with my discussion with john.

 

John

 

Thank you for you time and information.

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Bignose

 

If you would read the previously posted axiom that might clear things up.

I've read this whole thread. And I've seen what you did there. You've added a 2nd dimension. Which doesn't say anything about a regular 1-D number line.

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My apologies if you did not say that zero apples means nothing.

 

I repeat: This is what is known as a "straw man" fallacy. No one says that zero apples means nothing; it just means no apples.

 

And, again, I repeat: the fact that it is impossible to have "nothing" (a pure vacuum or whatever) in our universe is irrelevant. There is nothing that says that mathematics has to be limited to what is physically possible in reality. So if I choose to use 0 to represent the complete absence of anything (i.e. nothing) then I am free to do so.

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Strange

 

It is impossible to represent anything that does not exist. Any symbol exists, therefore the thing it represents must exist. Otherwise it is a contradiction to its own definition. Individuals have claimed zero represents "nothing". I am glad you agree with me, that it does NOT represent nothing. Maybe then you and I could move on to the next point? Perhaps Strange you and I could start from the beginning of the intention of this thread. Would you give me "again" a reason why zero must remain undefined.

 

 

Bignose

 

I had no intentions of talking dimensions. I have only stated that for every A in S there exist a z1 and z2,.....etc.

Edited by conway
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It is impossible to represent anything that does not exist. ...

Rubbish: for example it's utterly trivial to write down a number that represents more "things" than there are electrons in the entire known Universe. Math is abstract, and can be used to describe reality - but doesn't have to confine itself to that reality. If you were physically drawing a line, you might (in "reality") be limited to making that line out of a finite number of atoms; but mathematically, there'd be an infinite number of points on that line.

 

 

... Would you give me "again" a reason why zero must remain undefined. ...

Sloppy language. Zero is defined. Division by zero isn't. And you've been shown why.

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pzkpfw

 

yes indeed, sloppy language by me. I apologize I meant division by zero. If "nothing" does not exist then it can not be represented, physically or abstractly. Because the abstract and the physical exist.

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Bignose

 

I had no intentions of talking dimensions. I have only stated that for every A in S there exist a z1 and z2,.....etc.

by making a z1 and z2, you'd made a 2 dimensional object. Because you have a number for each of the dimensions, z1 and z2. Please at least look at some vector development. You've done it exactly. You can't fix division by 0 in 1-D with a 2-D object. You can't have a z1 and a z2 without it being a 2-D object. You only get one thing, z1.

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Bignose

 

I understand what you are saying, and I agree. I do think however that it comes down to what we are defining as z1, and z2. Where as you are suggesting that they both are dimensions. I am suggesting only one is a dimension, while the other is a value.

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Bignose

 

I understand what you are saying, and I agree. I do think however that it comes down to what we are defining as z1, and z2. Where as you are suggesting that they both are dimensions. I am suggesting only one is a dimension, while the other is a value.

The simple fact that you are using 'the other' means that the second value is independent of the first one. Ergo, another dimension, in the mathematical sense.

 

Either, you are 1) using a 2-D object (and trying not to call it that) or 2) by trying to use this 'value', you are simply saying, "hey, I know that you tried to divide by 0, but really, you meant to divide by 1, right. 'Cause z2 = 1. That's what you meant. I'm going to just go ahead and use 1 then, ok?"

 

Either way, you haven't fixed anything. You've just shoved some new terminology in there, and didn't bother to worry about how this new terminology leads to other incompatibilities.

 

Look, I appreciate the effort. I can understand how unsatisfying just having something seemingly as simple dividing by 0 is left as indeterminate or undefined. But these band-aid fixes over it isn't the solution. There are very deep issues on how number theory is built that all need to be worked through. It is certainly possible to build a number theory with either of the two 'fixes' above. But it isn't possible to build one with those 'fixes' and have it be the same as the everyday common one. It just doesn't work that way. The everyday common one has left division by 0 to be undefined for good reasons, see the many numerous replies in this thread.

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Bignose

 

 

It is that A is composed of a quantity of defined value, "inside of" a quantity of defined space. That is...

 

A = (z1 A , z2 A) = (A as value, A as space) = A

 

2 = (z1 2 , z2 2) = (2 defined values, 2 defined spaces)

 

0 = (z1 0 , z2 1) = (1 undefined value, 1defined space)

 

1 = (z1 1 , z2 1) = (1 defined value, 1 defined space)

Edited by conway
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It is impossible to represent anything that does not exist.

 

Really. So all those representations of unicorns prove that unicorns exist. Got it. Thanks for clarifying that.

 

Any symbol exists, therefore the thing it represents must exist.

 

Let M represent the number of mammoths on Mars ...

 

I am glad you agree with me, that it does NOT represent nothing.

 

That is not what I said. I said that saying you have zero apples, does not mean you have nothing. I also said, you can choose to use zero to represent nothing.

 

For example, consider a hypothetical universe containing no matter or energy. Then this universe contains nothing: the number of electrons is zero; the amount of energy is zero; etc. Note that there are mathematical models of such universes (they are useful for exploring the implications of the Einstein Field Equations) and so according to you they must exist.

 

Perhaps Strange you and I could start from the beginning of the intention of this thread. Would you give me "again" a reason why zero must remain undefined.

 

I, and many others, have given you several reasons. Do you need more?

 

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Perhaps Strange you and I could start from the beginning of the intention of this thread. Would you give me "again" a reason why zero must remain undefined.

 

I, and many others, have given you several reasons. Do you need more?

 

 

 

Hey, Strange, did you really say zero was undefined or was it division by zero?

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Hey, Strange, did you really say zero was undefined or was it division by zero?

 

Well spotted.

Would you give me "again" a reason why zero must remain undefined.

 

Zero is not undefined. It is very well defined. One simple definition is that it is the cardinality of the empty set. (But I suppose you will struggle with that as nothing is ever truly "empty".)

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Strange

 

Unicorns exist in an abstract sense. That does not mean they are real. There are M mammoths on mars abstractly speaking. Abstraction exist, but is not real. A universe containing no matter an no energy is not empty. It still has dimensions. Therefore is not nothing. You can not conceive of a thing that does not exist. Nor can you represent it.

 

To clarify....Give me again what you consider the be the BEST reason why / by zero must remain undefined. Again also I suggest that the definition of zero is undefined value, defined space. What then Strange is your definition of zero?

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To clarify....Give me again what you consider the be the BEST reason why / by zero must remain undefined.

 

I suggest you read through this thread. There are some very good reasons.

 

Again also I suggest that the definition of zero is undefined value, defined space. What then Strange is your definition of zero?

 

Do you have problems reading?

 

Zero is not undefined. It is very well defined. One simple definition is that it is the cardinality of the empty set.

Or maybe we are into that common trope:

 

Speculator: "please show why my idea is wrong"

A: <detailed explanation in the flaws in the argument>

B: <further analysis and other reasons why the idea won't work>

Speculator: "well if no one can show where I am wrong, my theory must be correct."

A: "No as I said, ... "<repeats detailed refutation>

C: "And in addition ... " <adds further analysis of the flaws>

Speculator: "If you think my theory is wrong, can you provide some specific reasons."

A, B, C, D, E and F repeat ad nauseum the explanations with yet more evidence, mathematics, analogies, etc

Speculator: "So no one can show my theory to be wrong."

A universe containing no matter an no energy is not empty.

 

Yes it is.

 

 

It still has dimensions. Therefore is not nothing.

 

It is not nothing, it is an empty universe. It contains nothing. Many of your comments are very sloppy like this. I'm not sure if this reflects the lack of clarity of your ideas, or problems with reading.

Unicorns exist in an abstract sense. That does not mean they are real. There are M mammoths on mars abstractly speaking. Abstraction exist, but is not real.

 

So "nothing" is an abstract concept and therefore, by your definition, it exists.

Edited by Strange
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Bignose

 

 

It is that A is composed of a quantity of defined value, "inside of" a quantity of defined space. That is...

 

A = (z1 A , z2 A) = (A as value, A as space) = A

 

2 = (z1 2 , z2 2) = (2 defined values, 2 defined spaces)

 

0 = (z1 0 , z2 1) = (1 undefined value, 1defined space)

 

1 = (z1 1 , z2 1) = (1 defined value, 1 defined space)

Explain again how these aren't 2D objects? (A, A), (2, 2), (0, 1), and (1, 1)...

 

You've explicitly listed 2 dimensions, z1 and z2. These are 2d vectors. The 0 vector in 2D is usually (0, 0). You're just trying to change the definition without taking into account the consequences.

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Strange.

 

This post has nothing to do with "my" theory. Such a post would be against the rules. I am trying to understand why / by zero is undefined. If you feel that I "just" won't get it, then stop responding. Maybe others will continue to help me. Maybe not. I am aware that many reasons have been given in this post as to the "reason" for /0 remaining undefined. I personally either A)no not understand them B)disagree with them. This is my inherent right to try to "finalize" this idea with in my own mind. Thank you Strange for your time in this matter. I am sorry for it to have been related to anything other that my inability to understand and or accept / by zero.

 

I will also raise your conversation scenario with another conversation scenario

 

caveman- "Hey I got this idea the world is round"

caveman2- "That's stupid"

caveman- "Well here's why, tell me what you think. Specific reason A,B,C,D"

caveman2- "Well I know more than you, and your just wrong."

caveman-"But why?"

caveman2- "Shut up poopy head"

 

Bignose.

 

Because they are ONE object.

 

A = one object = composed of z1 and z2 = z1 is value inside of z2 which is a dimension.

 

z1 and z2 are two objects, but they compose ONE object.

 

such as a cheeseburger has many objects, but is ONE object.

 

two objects requires two spaces and two values

 

one object has one space and one value......but two things.

Edited by conway
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Bignose.

 

Because they are ONE object.

 

A = one object = composed of z1 and z2 = z1 is value inside of z2 which is a dimension.

A vector is one object, too.

 

A rose by any other name would smell as sweet.

 

By your own words, you have a an object with two components, z1 and z2. This is a vector: https://en.wikipedia.org/wiki/Euclidean_vector

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Strange.

 

This post has nothing to do with "my" theory. Such a post would be against the rules. I am trying to understand why / by zero is undefined. If you feel that I "just" won't get it, then stop responding. Maybe others will continue to help me. Maybe not. I am aware that many reasons have been given in this post as to the "reason" for /0 remaining undefined. I personally either A)no not understand them B)disagree with them.

 

Then, perhaps, a more constructive approach would be for you to say exactly what you do not understand, or what you disagree with. Then people could clarify those specific aspects for you.

 

Just ignoring the reasons given and requesting other reasons is not going to help anyone. The chances are you wont understand or like those and will just ignore them to.

 

So, I would suggest you ask questions about the parts you don't understand ...

 

 

I will also raise your conversation scenario with another conversation scenario

 

Yes, but unlike my example, which happens with tedious regularity, yours never happens.

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Strange

 

I certainly agree you scenario happens more than the one I posed. I have asked questions. Many times. I have gone out of my way to bring it back to the very specific thing in which I do not understand. Now you and I may talk philosophically about ,dividing by zero with apples, but this will never do the conversation justice. As you have pointed out it only leads to a continues debate. So then I again evidence post #17, in which all field axioms are listed. I only add one axiom, requiring that all other axioms listed stay the same. So then what zero is or isn't, is not really of consequences. The axiom in which I gave allows for * and / by zero. So if this is so,(maybe it isn't), then the only thing stopping it would be "another" reason why / by 0 must remain undefined.

 

Bignose

 

I am glad that you chose a vector as an example. It perfectly describes what I am suggesting. While "part" of a vector is a dimension, the other "part" of the vector is velocity. So then again a value and a space, composing one thing...a vector. If you wish to consider a mathematical vector like the one you linked, it also seems the same to me. A length, space, and a "direction", value. Here we will certainly debate "direction", as it seems to me that it is a "potential" dimension, therefore a value.

Edited by conway
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Bignose

 

I am glad that you chose a vector as an example. It perfectly describes what I am suggesting. While "part" of a vector is a dimension, the other "part" of the vector is velocity. So then again a value and a space, composing one thing...a vector. If you wish to consider a mathematical vector like the one you linked, it also seems the same to me. A length, space, and a "direction", value. Here we will certainly debate "direction", as it seems to me that it is a "potential" dimension, therefore a value.

It doesn't matter what units you use in your vector. Volume, velocity, mass, whatever. The fact is that it is still a vector. And you are trying to resolve an issue in the 1st component by invoking a second component.

 

This doesn't fix division by 0 on the plain old regular 1-D number line. 1-D. Where there doesn't exist multiple dimensional objects. That's what the 1-D space is. As far as the 1-D space is concerned, 2-D things don't exist. And you can't 'fix' something by invoking that second dimension. At least not while still claiming it is the same space. You've invented a new space. Huzzah. Just don't expect results from it to apply to the regular plain old 1-D number line.

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Bignose

 

What say you then to the idea that a 1-d object exist and is also composed of a value. Is this possible? If so then can I not represent both the value, of the object, and the 1-d space of the object?

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Bignose

 

What say you then to the idea that a 1-d object exist and is also composed of a value. Is this possible?

Yes, as a 2-D object, like a vector. You don't get both. It is either 1-D and you only get 1 component (number), or is it higher dimensional and you get multiple components (numbers). You can't have 1-D with 2 components.

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