Infinity and Infinitesimals - Part II

By: LariAnn Garner
Submitted: 2007-01-17 16:26:59
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So what of numbers, such as 2, 11, -1028, or 15i? While the conventional understanding of numbers is that they can be arranged in a series such that at one end you have the smallest and at the other end you have the largest, this concept can be true only in a relative sense, as in the comparison of one finite quantity to another finite quantity. In terms of Reality, all finite numbers, including so-called whole numbers, are fractional.

What this means is that 2 symbolizes the 1 divided into two parts, each of which is smaller than the 1, and 11 symbolizes the 1 divided into 11 parts. Contrast this with the conventional understanding that 2 is twice as many as 1, and 11 is eleven times as many as 1. The observation that 2 is twice as many as 1, for example, is a comparison between two fractions of the One, and that is what yields the illusion of greater and lesser. This is easier to grasp when you recognize that the symbols 2 and 1 are actually 2 ⁄ ∞ and 1 ⁄ ∞. So, 2 ⁄ ∞ is greater than (>) 1 ⁄ ∞, but this is a relative comparison only because so long as Infinity (∞) remains a part of each fraction, the actual values are infinitesimal. Leaving Infinity in each fraction references the Reference (i.e. ∞ ⁄ ∞, the One), so in order to make space/time sense of these numbers, 1 ⁄ ∞ and 2 ⁄ ∞ must each be multiplied by ∞ in order to remove it from the equation. You are then left with 1 and 2 as relative quantities.

Consider an example using a group of apples. To evaluate a group or quantity of apples, the universe of apples must first be referenced by default in order to establish a relative measure and thereby give meaning to it. This universe of apples is a finite quantity, so it can be used as a relative reference without yielding infinitesimals. Within the universe of apples, a portion of it, such as eleven apples, is a fraction of, not more than, the universe. The group called "eleven apples" represents a subset of the universe of apples, so to measure eleven apples you must divide that universe such that you have a quantity you can call "eleven".<

Furthermore, you cannot reference the universe of apples without first referencing the universe of fruits in order to establish what an apple is, relative to all other fruits! This referencing must go on until you, at long last, reference the Reference, Infinity. However, since a measured quantity becomes infinitesimal when compared to Infinity, those working with finite quantities will stop short of any referencing that involves Infinity.

So, in this example the universe of apples is symbolic of Infinity, and any subset, group, or quantity which is less than the entire universe is a fraction of that universe, symbolic of finite numbers.

Since the infinitesimal cannot exist without relative measurements, the infinitesimal is an artifact of the illusion of separation, and is dependent upon the concept of limitation, which is also illusory.

The primary reason why I am proposing that numbers greater than one are in fact fractional is the basic mystical Truth that All is One. Thus, anything that does not equal All is less than, or smaller, than One. One, therefore, must be the center, and all numbers we are used to thinking of as less than one as well as all numbers we are used to thinking of as greater than one are fractional in nature, and represent dimensional iteration of the One. Therefore, this One, or center, has to equal Infinity in order to be greater than any finite number.

With this in mind, we find that values as a series can be represented on a polaric axis with One (1) at the center, all numbers "smaller" than 1 on the left side of the center and all numbers "larger" than 1 on the right side of the center. Since this center is actually the One, or ∞ ⁄ ∞ , we see that all numbers, whether on the left or the right of center, are infinitesimals, having Infinity as their denominators.

Using this new coordinate axis, what is the difference between two points labeled 0.5 and 2 on this axis? The answer is that they are equivalent in value, because 0.5 is 1/2 of the One and 2 is the One divided into two equal parts. The symbols simply distinguish which "side" of the axis the measurement is being made along. Of course, Reality is that the One cannot be divided at all, so the idea of dividing the One is really the dividing of a unit, or 1, not Infinity.

(continued in Part III)

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