# Numerus “Numerans-numeratus”

#### AndyDora

Meadows are being investigated for avoiding division by zero errors. I'm asking for concrete examples of when $\dfrac{a}{0}=a$ is a desirable result. What does it mean? Just because it is possible to do something does not mean that there is value in doing it. It is possible to learn Klingon. Some people do learn Klingon. But, in general, it is not a valuable language. There are very few speakers and very little literature. Other than as an intellectual curiosity, it serves little purpose.

Is division by zero meaningful? If Bob has five friends and he divides them into zero groups, what does that mean? This is where my mind was when I said it is as if no division happened. But, I am not sure that answer is desirable. There is value in a computer generating a division by zero error. I actually work as a software developer. I've never been in a situation where I thought, I wish I could divide by zero! It has never had value in my work. Under what conditions would software be better if division by zero were possible?
I can not answer this at this time. As you have imagined. Also...another person has continued asked what the goal is. I find that this also keeps slithering away from me. I can say this...

I am under the impression that...

Any system that more accurately describes reality, than the current system...then holds value...regardless of one's ability to expand upon it.

The last link I gave...is proof that what I have written more accurately describes reality...at least in my opinion.

I can imagine a conversation between Pythagoras and any odd person, in which Pythagoras said the world was round. It did more accurately describe reality...but it made no empirical difference at the time....

In any case...I understand that I must find more reasoning and value......this has been an excellent forum interaction. Thanks to all.

#### SlipEternal

MHF Helper
The last link I gave...is proof that what I have written more accurately describes reality...at least in my opinion.
I'm not sure what this sentence means. If dividing by zero "more accurately describes reality", then what does it mean to divide by zero? You explain the process by which you move numbers around, but how does that "describe reality"? When, in reality, do we divide by zero? I wish you the best of luck. You have clearly spent a lot of time thinking about this, so I hope it pans out for you.

1 person

#### AndyDora

If Bob has five friends and he divides them into zero groups, what does that mean?

This is an example YOU gave...that divides by zero....And reality tells us how many friends Bob has...he has five...even and especially after he divides them into zero groups...just as if he divided them into one group he still has 5 friends......

This is re-hashing...and doesn't deserve a response..I would not annoy you Slip....thank you very very much for you time and considerations...

#### AndyDora

*A proposed solution for the reasoning and purpose of Numerus Numerans Numeratus

It is well known the response Siri gives if asked to divide by zero. It is well known why. It is considered a joke. It is possible to solve these issues both semantically and mathematically without flaw. The insignificance of which cannot be overstated.

I will offer a few semantic examples of Siri responses, and the “isomorphic” representations to each. Showing hopefully, the possibility and insignificant necessity for Numerus Numerans Numeratus.

It is known that any number divided by zero is undefined. Therefore, Siri is forced to give the “well known” answer she is programmed to. Of course, one will note that if asked to multiple 0 by 0, Siri can answer the question as 0 without any apparent confusion.

Semantic statements.
If I have zero cookies and divide them by zero friends…
The answer: Doesn’t make sense…etc…(plus a joke and insult).
Isomorphic semantic statement.
If I have the numerical value of zero cookies and divide it into the dimensional unit of zero cookies…

If I have one cookie and divide it by zero friends…
Isomorphic semantic statement:
If I have the numerical value of one cookie and divide it into the dimensional unit of zero friends…
The answer: I have one cookie…plus some extra space….(see we can keep the jokes)

If I have 2 cookies and divide them by zero friends...
Isomorphic semantic statement:
If I have the numerical quantity of 2 cookies and divide them by the dimensional unit of of zero friends...

If I have zero cookies and divide them by two friends...
Isomorphic semantic statement:
If I have the numerical quantity of zero cookies and divide them by the dimensional unit of two friends...

Assertion:
Therefore: it is possible to allow semantic solutions for “mathematical” impossibilities…without violating the inherent construct of mathematics. The real issue is the computer programming of Siri, this then can also be used to offer solution for division by zero errors.

A semantic and mathematical unification of insignificant proportions.

*On a final note...clearly Siri is wrong...I have friends...and I spend a vast amount of time thinking about these things.

#### HallsofIvy

MHF Helper
I can imagine a conversation between Pythagoras and any odd person, in which Pythagoras said the world was round. It did more accurately describe reality...but it made no empirical difference at the time....
I don't know that Pythagoras ever worried about whether the world was round or not but there was plenty of evidence that the world was round at that time. Aristotle gave several arguments for the earth being round.

One is that when a ship sails away from the shore it appears to get lower and lower in the water, not just smaller. Another is that, during a lunar eclipse, the shadow of the earth on the moon is round (Aristotle specifically mentioned that). Aristotle also remarked that, as you move south, the stars that you can see at night change- the northernmost stars "disappearing", new stars appearing in the south. Aristarchus, who lived about 350 BC, actually calculated the radius of the earth very accurately. Living in Cairo, he heard that, at a certain place, in midsummer, the sun shown directly down a well and that vertical sticks cast no shadow (the place was on the "tropic of cancer", the farthest north that the sun "moves"). He hired a man to measure the distance from that place to Cairo and measured the length of a shadow of a stick at midsummer in Cairo. That allowed him to calculate the radius of the earth.

#### SlipEternal

MHF Helper
The insignificance of which cannot be overstated.
From context, this sentence likely means the opposite of what you want it to mean. If something's insignificance cannot be overstated, that is very insignificant. I believe you meant, "The significance of this cannot be overstated."

Anyway, what I am struggling with is the same thing that I was struggling with before. Just because you "can" do something in mathematics does not mean that it necessarily "makes sense" to do that or that you "should" do it. You keep saying that division by zero "better describes reality". Yet, in the instance of slopes of lines, the notion of division by zero quickly degenerated into meaninglessness. While mathematicians do divide quantities into groupings, I am not following the argument that it "better describes reality" that zero has a space equal to the space granted to 1, but $\dfrac{1}{4}$ has less than that. I am not understanding the logic behind it. I am not understanding the purpose for it.

So, my question is still how does it more accurately describe reality? I know you are trying to answer exactly that question, and I apologize, but I am still not getting it.

1 person

#### AndyDora

From context, this sentence likely means the opposite of what you want it to mean. If something's insignificance cannot be overstated, that is very insignificant. I believe you meant, "The significance of this cannot be overstated."

Anyway, what I am struggling with is the same thing that I was struggling with before. Just because you "can" do something in mathematics does not mean that it necessarily "makes sense" to do that or that you "should" do it. You keep saying that division by zero "better describes reality". Yet, in the instance of slopes of lines, the notion of division by zero quickly degenerated into meaninglessness. While mathematicians do divide quantities into groupings, I am not following the argument that it "better describes reality" that zero has a space equal to the space granted to 1, but $\dfrac{1}{4}$ has less than that. I am not understanding the logic behind it. I am not understanding the purpose for it.

So, my question is still how does it more accurately describe reality? I know you are trying to answer exactly that question, and I apologize, but I am still not getting it.
Yes...I was being sarcastic...I do consider it significant. But I did not really expect much progress with this last post.(hence the sarcasm)

1/4 does NOT have "less" space then 1

1/4 had a dimensional unit quantity of (_,_,_,_)
(_,_,_,_) is more than (_)

however...

Yes (_) is the same amount of "space" for 0 and for 1
The difference is...I put a quantity of 1 in it or a put a quantity of 0 in it.

With this last bit...I should have shown you how it more accurately describes reality. Siri, nor mathematics can give an answer to 1 cookie divided by 0 friends.
Yet we can actually perform this operation in reality...and physically see the result.

I will continue to try...I expect that if and when I have any success in this regard you will let me know.

Thanks Slip.

Continued examples.

If I have 5 friends and put them into (_) ... a "space" or the dimensional unit of 0, or of 1

I still have 5 friends...all in the same space

If I have 0 friends and put them into the (_)...or "space" or the dimensional unit of 0

I still have 0 friends....

I NEVER EVER had an "undefined" amount of friends....in either case...in fact...no one ever had undefined amount of friends in the history of humanity...they may not know how many they have...but the amount they have is always definable...as zero or otherwise.

Therefore a more accurate description.

#### SlipEternal

MHF Helper
Yes...I was being sarcastic...I do consider it significant. But I did not really expect much progress with this last post.(hence the sarcasm)

1/4 does NOT have "less" space then 1

1/4 had a dimensional unit quantity of (_,_,_,_)
(_,_,_,_) is more than (_)

however...

Yes (_) is the same amount of "space" for 0 and for 1
The difference is...I put a quantity of 1 in it or a put a quantity of 0 in it.

With this last bit...I should have shown you how it more accurately describes reality. Siri, nor mathematics can give an answer to 1 cookie divided by 0 friends.
Yet we can actually perform this operation in reality...and physically see the result.

I will continue to try...I expect that if and when I have any success in this regard you will let me know.

Thanks Slip.

Continued examples.

If I have 5 friends and put them into (_) ... a "space" or the dimensional unit of 0, or of 1

I still have 5 friends...all in the same space

If I have 0 friends and put them into the (_)...or "space" or the dimensional unit of 0

I still have 0 friends....

I NEVER EVER had an "undefined" amount of friends....in either case...in fact...no one ever had undefined amount of friends in the history of humanity...they may not know how many they have...but the amount they have is always definable...as zero or otherwise.

Therefore a more accurate description.
My question is, if you are dividing your friends into one dimensional unit, are you dividing by zero? Or are you dividing by 1 and saying that you are dividing by zero? Math allows you to create definitions that do NOT match reality. Why do you feel that zero should have "one dimensional unit"? In what way does zero offer "space"? When you say you are dividing by zero, it appears you are simply replacing the division with a division by 1, and then after the fact, you are justifying it with notation. I have not seen how this notation actually represents reality. So far, everything you are offering feels very circular. You say the notation better describes reality, but it is a reality based on a definition that you say is needed to describe the notation. Perhaps I am missing something. Please do not think that I am just trying to be argumentative. I am really trying to grasp what you are saying, but at the moment, it is eluding me.

1 person

#### AndyDora

My question is, if you are dividing your friends into one dimensional unit, are you dividing by zero? Or are you dividing by 1 and saying that you are dividing by zero? Math allows you to create definitions that do NOT match reality. Why do you feel that zero should have "one dimensional unit"? In what way does zero offer "space"? When you say you are dividing by zero, it appears you are simply replacing the division with a division by 1, and then after the fact, you are justifying it with notation. I have not seen how this notation actually represents reality. So far, everything you are offering feels very circular. You say the notation better describes reality, but it is a reality based on a definition that you say is needed to describe the notation. Perhaps I am missing something. Please do not think that I am just trying to be argumentative. I am really trying to grasp what you are saying, but at the moment, it is eluding me.

I think your question is very valid.

If I am comparing these two expressions...

n/(_) : n/(_)

Yes, I agree, there is no way to say which is zero and which is the number 1.

However the op shows that it can be expressed as...

n/(0_) and n/(1_)

also as:

n/(0) and n/1

Where:
n/0 = n/0_ = n/(_)

Where:
n/1 = n/1_ = n/(_)

This then shows exactly when (_) is the dimension of zero, as opposed to the dimension of 1.

So technically when we divide in this system by zero, or any number...it is not a numerical quantity it is a dimensional quantity, that is "placed into".

So if I divide a cookie or zero cookie into the dimensional space of zero, or the dimensional space of any number....that cookie is still there.

So I may only say the cookie divided into the "space" of zero, or the cookie divided into the "space" of 1. "Both of which are the same"

So in any and all semantic statements, I must clarify which "thing" is the cookie, or numerical value, and which "thing" is the space, or dimensional unit.

I claim that zero has space...because of many reasons...

I also claim zero is the absences of a given numerical quantity...(as is currently accepted)...but it is also a quantity of dimension.

"Nothingness" does not exist...so if zero is not "nothingness" and it is also the absence of a numerical quantity...what then is it...the only remaining option is a dimensional unit quantity.

Also the equation 1 + (-1) = 0....proves the space of zero...and that it is equivalent to the space of 1.

We never have a "number" unless a numerical quantity and dimensional unit quantity are "together". This is so in the math and so in the semantics.

I hope I have understood your questions. I hope I have answered them.

Thanks!