Every number, expressible and inexpressible sits upon a template for organizing the numberness of the number. We call this template a base. The base of a number is a power series which escalates to infinity in one dimension, (it's post decimal dimension), and toward zero in the other pre-decimal dimension.

Here we have a vector going in either direction, toward infinity, and toward zero. For instance, base 10 mathematics uses 10 as its base and thus everything is power of 10. Behold:

116,651 = 1*10^5 + 1*10^4 + 6*10^3 + 6*10^2 + 5*10^1 + 1*10^0

Now if we wanted to add .1234 to this number our power series would extend like so:

1*10^-1 + 2*10^-2 + 3*10^-3 + 4*10^-4.

Now, when we represent the number, we only consider the segment between the highest and the lowest place value, where 1^10^0 would always be considered the origin of both vectors. So, when you are seeing a number, you are always only seeing part of an infinite series which is lit up between extremes.

~~~

Now in Base-2, or Binary, the same rules hold true as in base 10, except that everything is a power of 2.

So instead of the chain extending like this:

1,10,100,1000,10000 ...

It extends like this:

1,2,4,8,16,32,64,128,256,512,1024,2048 ...

&

.5, .25, .125., .0625, ...

~~~

Our Base 10 system of representations is not without its paradoxes. Behold:

1/3 = .333333...

1/3 = .333333...

1/3 = .333333...

~~~~~~~~~~~~~~~~

3/3 = .999999... = 1

In such an instance the bare bones of our structure to contain the Number is laid bare, extending infinitely toward 9*10^-INF which is also Zero. So, even with an eternity to work with, we can never finish the task of writing this number.

~~~

What is the Point?

Well, just that the number seems to be describing the relationship of one thing to another in a very specific sequence, where the sequence conveys a large part of what the representation refers to.

Suffice it to say, when we introduce the concept of number it's a how much/how many indication. Each number occupies one infinitessimal point on a line known as the "real number line". The end points (which do not fall on the line) are INFINITY and -INFINITY.

The number is a point. A geometric object which describes itself only in relation to other objects and as part of some system.

Really, an odd thing to contemplate.

*Scratches head*

I will drink more coffee.

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