2) These phenomena, as composed of phenomena, relate to other phenomena and in turn compose other phenomena.
3) A phenomena, as both being composed of and composing further phenomena, observe the phenomena as relation.
4) Relation, through the phenomena, exists as individuation where a phenomena exists if and only if it simultaneously separates itself from other phenomena while unifying other phenomena. This act of separation results in the form of unity, while the act of unifying results in a form of separation.
Ex: The separation of a line results in multiple lines as unified forms.
1→ (1,1)= 2
The unification of multiple lines results in the form of a separate line separate from the multiple lines.
(1,1) → (1) = 1
5) Individuation as simultaneous separation and unification is the synthesis of limit through movement as localization.
6) Localization as limit is movement, with the nature of limit inseparable from movement.
7) The nature of limit existing through limit observes that limit exists through itself as a ratio of movements.
These movements exist if and only if they are directed with direction existing as one movement relative to another movement.9) Localization as limit is movement as direction.
10) Movement as direction is consistent (or continuous) depending upon its relation to other movements as direction. Continuity is dependent upon the inherent proportion of one movement to another.
Ex: 1(1 → (n→∞)) is a continuous number line that exists as 1 line in itself. If it folds into 2 equal numbers lines:
((1(1 → (n→∞))=1(n_1 → (n→∞)))= (1(1 → (n→∞)),1(n_1 → (n→∞))))=(2,1/2)
each line exists as ½ the original line with the original line being the standard for the 2 lines resulting from it. Simultaneously, at the same time in a different respect, these 2 lines become a standard from which other ratios exist. 1/1 and ½ in turn observe an inherent nature of ratios which stem from relations as a form of individuation. Each ratio exists as a unit in itself form which other ratios exist.
11) Considering the origin of limit, form which other limit extend as ratios through relation, must be both 1 and continuous and the limits which exist as ratios through it must follow the same form and function they too are both 1 and continuous when observed as localized entities in themselves. In these respects limit exists through limit with any inherent change being a localization of the limit itself which is infinite.
12) Each ratio, as a limit, exists relative to other ratios, as limits which form the phenomenon in itself as a ratio.
13) Each ratio as a limit conducive to movement as direction through localization, exists as an inherent qualitative unity in itself being conducive quantitatively to 1. Time through multiplication as “y added/unified x times” and “x divided/separated y times”, exists as a form of individuation conducive to finiteness with finiteness being multiple infinities extending from a single infinity.
Finiteness as a an infinity implies a contradiction at first glance but considering a finite reality is merely a ratio of 1 infinity, finiteness can be observed as separation through replication (or multiplication).
14) The basic limit as movement through direction is 1. The qualitative unity of the limit, and it quantitative nature as 1 observes the 1d line as the foundation of all phenomena.
Ex: The progression of numbers exists if and only if it is premised in a linear direction.
15) The limit as qualitative unity and quantitative 1 observes the limit itself as a positive neutral median of both quantity and quality.
16) The limit as either quantity or quality, in the respect it forms the boundaries of quantity and quality as phenomena of measurement in themselves, exists as a strictly neutral median.
17) The limit as neither quantity nor quality in the respect it forms neither observes an inherent potential nature to quantity and/or quality being limits in themselves.
18) The limit as movement through direction (or localization) necessitates the “being que being” or “phenomena through phenomena” as “limit through limit” observes the base pre-socratic notion of limit existing through limit.
Localization can be viewed as directional in the respect that the localization of a phenomena causes it to project itself through time as a direction, considering the premise of the time as a linear structure in itself is direction hence acts as a form of individuation in its own right.
19) The premise of “the line through line”, under limit through limit, observes direction as movement resulting in the repetition of individuation under the terms “frequency”. This repetition of individuation, as direction through direction, results in the line folding through the line. The folding, as a frequency, results in the frequency as movement through direction, hence limit in itself.