Quantitativeless Numbers

Well, what do 0 and infinity have in common? Besides being two of the oddest "numbers", they represent something other than a set quantity.
Numbers are representative of quantity. We used them to make order from chaos, to change a pile of fruit into a divisible stock of food. |----| is one. |--------| is two. All numbers follow this rule; two points segregating an infinity into a quantity.
So, are 0 and infinity numbers? They do not represent quantities, and they break many rules that all numbers follow. So, why do we include them in our ideas?
First, let's look at all 3 of the quanititaveless numbers I can imagine right now.

                                     ∞Infinity∞
Infinity is what you get when you take any quantity and repeat it infinitely. 3 repeated infinite times is equal to 1,000,000 repeated infinite times. Maybe an idea is starting to take shape in your head now; the idea that in terms of infinity, all rules of equality break down. If you had 2 infinite lines, they would be equal since they had the same length of infinity. Now, imagine that you take one of these lines and cut it in a random place. Is it now shorter than the "whole" line because the whole line continues where the previous one leaves off? No. This is the magic of infinity. You can divide it any number of times. You can make as many different sets of infinity as you like, and they will always be equal.

                                  ˝Infitesima˝
You can think of infitesima as the infinitely small. It's what you get when you take any number and divide it by infinity. The infitesima is best defined by Euclids first axiom: "A point is that which has no part". Since you have divided by infinity, and as you have seen before, any manipulation of infinity by a number results in more sets of infinity, any manipulation of the infitesima by a number does nothing. An infinitely small object will always be infinitely small no matter how many billions of infinitely small objects you add to it. A way of looking at it is like this:
 _
.01. This is a decimal followed by an infinte amount of repeating zeroes, than a one. It represents an infitesima.
Here's a quick way to understand how this is applicable in the real world.
        _
1/3=.3
                _
(1/3)*3= .3 * 3
     _
1=.9

So, what can you add to an infinte amount of 9's to make it zero? Well, you'd need an infinitely small number. You'd need infitesima. Without it, logic breaks down.

                                    0Zero0
Zero. It's the most popular of the quantitativeless numbers. Dividing by it results in a breakdown of logic, and mulitplying it eradicates any number. It is the most easily understood of the quantitaveless numbers, for while others are a more abstract type, this is literally without quantity. It is zero. I'm sure you already understand this well enough.



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Now, for the finale. Quantitaveless math axioms.

let x represent any number at all.

The Law of Self Morphism-
x*infinity=Infinity
x*infitesima=Infitesima
x*zero=Zero

The law of quantitativeless manipulation-
infinity*infitesima= X
zero*infinity=Zero
zero*infitesima=Zero

The law of inverse infinity-
x/infinity= Infitesima
x/infitesima=Infinity


These may seem utterly useless, but it's very interesting. It's how things beyond our normal comprehension work.
Everything is made of infinite infitesima, which really illustrates the different sizes of infinity.

I'll post on real world application, like dividing by zero, later.