I am getting more and more confused. To me, it is seemingly arbitrary how you decide how much "space" zero has. Why did you arrive at a space of 1? Why not the same space as 2? What makes the space of 1 correct? Why does 2 not have the same space as 1? It does not take 2 space to "move past" it on the number line. So, what makes the space of 2 equal to _,_? And why would it be bad if zero had no space? It still has a numerical value, and so addition and subtraction that yield 0 still will make sure not to miss it on the number line. You start at two and go three numerical units to the left. Why would you need space for the number zero at all?

Let's consider measure theory. Measure theory takes careful precautions to ensure that a single number (or point) does not take up any measurable space. If each individual number did take up space, then integration and much of advanced statistics would break. So, conceptually, I am having a hard time with the notion that you want to specifically give space to each number. How would this work with advanced mathematics? Is all analysis and topology wrong? Or do numbers not have space when you are studying measure theory, analysis, topology, advanced statistics, etc.?

Edit: It is not necessarily a bad thing if you decide that all of these branches of mathematics are wrong so long as you can recreate them using your number system. But, the fact that they all break and it is unclear if they can be recreated would give any mathematician heart palpitations at the thought of a number system that did not directly correct some major underlying problem within mathematics. For instance, if your number system lead to a measure theory that would prevent odd occurrences like the Banach-Tarksi paradox, it might be embraced. Think about it from a purely psychological standpoint. If your number system were to ever be adopted, it would require enough people to agree with it that they start using it for other branches of mathematics. But, if it does not work with other branches of mathematics and they have a stable system that has worked for thousands of years, what motivation could they possibly have to even give your system a chance?

You scold me well, in the same manner as you have before. I can not offer what is considered "sufficient" reason to mathematicians. Yet...that is. But I am working on this. I can offer the reason that it provides solutions for questions Siri can not answer...as suggested.

Any time I use the term "space" or dimensional quantity unit....it's length and width remains abstract and undeclared. This is from the op.

I never claim zero has more than "a single" space. It is arbitrary...just as you say.(nor can you EVER define its' length and width).

But if you do NOT allow zero to have a single "space"...then you can not divide by zero, or multiple by it with products other than 0.

Therefore...at no time is there a violation in topology and measure theory...as they require length and width to "not" exist (within each number)...not the actual dimension itself. This I know is a philosophical point. But it is the exact thing you are asking me regarding the use of 0 with only "1" space.

It is that zero has a single quantity of dimension...it is not that it has more than that.

It is that (1) has a single dimension...of which a single numerical quantity inhabits.

It is that (2) has two single dimensions...each of which a single numerical quantity inhabits.

The only difference between 1 and 0....is that 1 has a numerical value assigned to a dimensional unit, or a single space.

Zero...just has not had a numerical value assigned to the "single space". That is why zero has a "single" space....as opposed to "two" etc...

I will investigate this paradox you suggest...very likely it is over me, and will take me much time...

Again...so far...I can only say this is good for a unification of semantics and mathematics.

I can only.... at this time.... say...it is now possible to divide by zero...semantically...without breaking the rules of mathematics.