# Numerus “Numerans-numeratus”

#### SlipEternal

MHF Helper
This has been very helpful. I will do my best to consider all of your advice. I am very appreciative of this.

If there is a multiplicative inverse for zero....then you violate a field axiom...I understand this is addressed in meadows by adjusting the field axioms. I do not wish to dissolve any field axioms. The point of this is to show that division by zero is possible period...and is a valid mathematical construct...thus anything more than a field, rings/meadows/wheels.... is not even needed. That is why you would want this. Also it as stated it unifies mathematics and physics....which perhaps it is convoluted....time will tell.

It was once convoluted..and pointless to claim the world was round...now it is the exact opposite.

It unifies semantics...and mathematics...and philosophy...that alone is why...the division by zero a by product.

of course these are my opinions....it remains that I am grateful for you advice, help and time.

Thank you Slip

If I say...."I have zero money in my account"

What does this statement mean?

It does not mean I have no money...just non in my account.
It does not mean I can not write a check...just that it will bounce.
It does not mean I have no account...just no money...
so what does it mean....

mathematics needs space and value to describe all numbers...otherwise it fails...philosophically...semantically...and physically...to describe our reality.
This is precisely what I mean, and could provide a good introduction to your work. Describing shortcomings you find in mathematics gives a great lead in to what you are trying to fix and why. I cannot say whether other mathematicians will agree with this, but hopefully it will give them a better understanding of why your theory deserves their attention.

#### AndyDora

This is precisely what I mean, and could provide a good introduction to your work. Describing shortcomings you find in mathematics gives a great lead in to what you are trying to fix and why. I cannot say whether other mathematicians will agree with this, but hopefully it will give them a better understanding of why your theory deserves their attention.
I will consider how to introduce this as the prologue. Thanks for this advice. I have not done so up to now, because I strive to keep it short...for obvious reasons. I do however understand and agree with your point here.

I find that mathematicians hate my example. That they literally hate me...for suggesting it. I am a philosopher. This alone causes them to hate me. No over usage of the word hate here either. This is sad.

Mathematicians and philosophers were born as siblings. They split along time ago. Mathematicians searching only for the concrete. Philosophers searching only for the abstract.

We must unify them...as it should be. Then we will bring back the glorious days of great thought...like we have seen with the ancient mathematicians who where in fact philosophers also.

Thus...

Numerous Numerans Numeratus

#### AndyDora

When I first began this journey I used the words space and value.....

See here...is an example of the necessity for this work...without the philosopher and mathematician love hub bub...

I have shown...perhaps yet not precisely...a mathematical relationship between substance and space.

Exactly the claim that couldn't be done.

DIVISION BY ZERO ? NORTH OF REALITY

#### topsquark

Forum Staff
When I first began this journey I used the words space and value.....

See here...is an example of the necessity for this work...without the philosopher and mathematician love hub bub...

I have shown...perhaps yet not precisely...a mathematical relationship between substance and space.

Exactly the claim that couldn't be done.

DIVISION BY ZERO ? NORTH OF REALITY
I don't recall that anyone has said division by 0 can't be done. You can indeed define it to have a meaning. But it does tend to destroy a few properties of number system you are working in.

-Dan

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#### AndyDora

I don't recall that anyone has said division by 0 can't be done. You can indeed define it to have a meaning. But it does tend to destroy a few properties of number system you are working in.

-Dan
I understand this. However if it can or can not be done was not what I was referring to with this last link. The NEED for it to be done is now what seems to be the question, and where I seem to be lacking...

I have spent much time working on those "destroyed properties" you mention. I have carefully shown in the revised and op editions (I hope) how all field axioms remain unchanged...except regarding zero (and even then only the identity changes, and infinitesimally so). Perhaps there is yet an error....but....I still think it can be done without "touching" a single axiom...as suggested...and so far shown (again I hope).

Are you of the accord that even if I could do so...such as in meadows and wheels..that it would still remain pointless?
I hope to add here a collection of examples where there is a point....after I have amassed and considered them deeply.

Truly thank you for your time.

#### topsquark

Forum Staff
I understand this. However if it can or can not be done was not what I was referring to with this last link. The NEED for it to be done is now what seems to be the question, and where I seem to be lacking...

I have spent much time working on those "destroyed properties" you mention. I have carefully shown in the revised and op editions (I hope) how all field axioms remain unchanged...except regarding zero (and even then only the identity changes, and infinitesimally so). Perhaps there is yet an error....but....I still think it can be done without "touching" a single axiom...as suggested...and so far shown (again I hope).

Are you of the accord that even if I could do so...such as in meadows and wheels..that it would still remain pointless?
I hope to add here a collection of examples where there is a point....after I have amassed and considered them deeply.

Truly thank you for your time.
Honestly I am still struggling with what your notation means. For example, 1 = (1, _) and 2 = (2,_,_) is still a big question mark. I've read over your posted articles but if the _ isn't a unit I'm not understanding it. It's probably clearly pointed out somewhere and I just didn't see the significance of it. For that reason I'll probably just let someone else make responses, at least until I feel I can talk intelligibly about it.

-Dan

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#### AndyDora

Honestly I am still struggling with what your notation means. For example, 1 = (1, _) and 2 = (2,_,_) is still a big question mark. I've read over your posted articles but if the _ isn't a unit I'm not understanding it. It's probably clearly pointed out somewhere and I just didn't see the significance of it. For that reason I'll probably just let someone else make responses, at least until I feel I can talk intelligibly about it.

-Dan
I fully understand and accept your view point. I have struggled to find a way to make this worth peoples time. Of course time is the most valuable thing we have. Thus the struggle....however...

Both the op and the revised addition share the first few sentences almost the same...stating clearly that (_) is a unit....and a dimension...so on...

Let all abstract numbers be defined exactly as concrete numbers.
Concrete number: A numerical quantity with a corresponding unit.
Let the corresponding unit exist as an abstract dimension notated with the use of (_).
Let the length and width of all dimensional units remain abstract and undeclared.
Let the dimensional unit be equal in quantity to the numerical quantity it corresponds to.
Let all numerical quantities inhabit their corresponding abstract dimensional units.
Let zero be assigned a single dimensional unit.

#### SlipEternal

MHF Helper
Honestly I am still struggling with what your notation means. For example, 1 = (1, _) and 2 = (2,_,_) is still a big question mark. I've read over your posted articles but if the _ isn't a unit I'm not understanding it. It's probably clearly pointed out somewhere and I just didn't see the significance of it. For that reason I'll probably just let someone else make responses, at least until I feel I can talk intelligibly about it.

-Dan
From what I can tell, his notation, while cumbersome, is an attempt to attach a physical interpretation to the division by zero that is unchanged when viewed through the other binary operators of addition, subtraction, and multiplication across all real numbers. While it is not explicitly stated, it appears that the physical interpretation of division by zero is "leave the original quantity alone" or maybe "don't do the division" since if you divide the quantity into zero groups, you never touched the original quantity. You basically did not do the division. I am in full agreement that the notation is confusing, and I still am not sure I grasp how or why it is necessary. But, suspending my disbelief and pressing onward, the overall gist made more sense than the specifics of the notation. The point of divergence between his theory and more well-known examples of algebras that allow division by zero (such as meadows and wheels) is that he is explicitly not defining $0^{-1}$ because that is where most theories run into problems. Unlike most systems with division by zero, he does not allow $\dfrac{0}{0} = 1$. He has $\dfrac{0}{0} = 0$. Now, if all divisions by zero resulted in zero, that would also cause problems and violate the field axioms, as well (see involutive meadows). But, treating division by zero as multiplication by one seems to avoid many of the algebraic problems that result from defining $0^{-1}$. I have not comprehensively looked into this, but I do not see anything glaringly off that would indicate it would fail. It still might, and I reserve judgment, but it is a novel approach to defining a system with division by zero at the very least.

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#### AndyDora

From what I can tell, his notation, while cumbersome, is an attempt to attach a physical interpretation to the division by zero that is unchanged when viewed through the other binary operators of addition, subtraction, and multiplication across all real numbers. While it is not explicitly stated, it appears that the physical interpretation of division by zero is "leave the original quantity alone" or maybe "don't do the division" since if you divide the quantity into zero groups, you never touched the original quantity. You basically did not do the division. I am in full agreement that the notation is confusing, and I still am not sure I grasp how or why it is necessary. But, suspending my disbelief and pressing onward, the overall gist made more sense than the specifics of the notation. The point of divergence between his theory and more well-known examples of algebras that allow division by zero (such as meadows and wheels) is that he is explicitly not defining $0^{-1}$ because that is where most theories run into problems. Unlike most systems with division by zero, he does not allow $\dfrac{0}{0} = 1$. He has $\dfrac{0}{0} = 0$. Now, if all divisions by zero resulted in zero, that would also cause problems and violate the field axioms, as well (see involutive meadows). But, treating division by zero as multiplication by one seems to avoid many of the algebraic problems that result from defining $0^{-1}$. I have not comprehensively looked into this, but I do not see anything glaringly off that would indicate it would fail. It still might, and I reserve judgment, but it is a novel approach to defining a system with division by zero at the very least.
Thank you very much for that. I understand well that contradicitons may still exist. But there are others helping me here. They nor myself have found them with this latest version....however.....

Let division be defined as the placing of a given numerical quantity, with subtraction, equally into each given quantity of dimensional unit. Then all numerical quantities in all dimensional units are subtracted except one.

This is in both versions given....This statement holds true regardless of the "numerical quantity and the dimensional spaces given"..thus

if the numerical quantity is (a)
if the dimensional quantity is (_)

Then the "act" of placing that (a) ,"zero or otherwise", into the dimensional unit quantity DOES occur....therefor there can be none of this..."don't really divide" stuff....

By defintion a multiplicative inverse MUST be a numerical quantity...thus (0) can not be a multiplicative inverse. As the numerical quantity of (0) is non existent.
By definition a multiplicative inverse MUST be a numerical quantity...thus (_) can not be a multiplicative inverse. As it is the dimensional unit quantity of 0

#### SlipEternal

MHF Helper
This is in both version given....This statement holds true regardless of the "numerical quantity and the dimensional spaces given"..thus

if the numerical quantity is (a)
if the dimensional quantity is (_)

Then the "act" of placing that (a) z"zero or otherwise" into the dimensional unit quantity DOES occur....therefor there can be none of this..."don't really divide" stuff....

By defintion a multiplicative inverse MUST be a numerical quantity...thus (0) can not be a multiplicative inverse. As the numerical quantity of (0) is non existent.
By definition a multiplicative inverse MUST be a numerical quantity...thus (_) can not be a multiplicative inverse. As it is the dimensional unit quantity of 0
You misunderstand. I was not talking about your notation. I was talking about the intuition behind it. Your notation is trying to give a representation to a division that is not happening. The idea that the result of the division is that you place the numerical quantity into a dimensional space is how you are representing the fact that you are assigning division by zero the result of the original numerical quantity. The result is equivalent to the division simply not happening. That is incontrovertible, regardless of what your notation accomplishes or the actual process by which you arrive at that result.

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