This will appear about the same as the 1 as infinite division thread, however comes at a seperate angle.

The definition of the work can be expanded, however here is a premise idea:

The folding function is an original idea, so it won't be found in textbooks...unless someone knows something I do not.

The resulting number line is in the attachment for further clarity.

One exists if and only if there is 1.

The existence of 1 occurs if and only if there is 1 and 1 occurs if and only if there exists 1. “Existence” is inherent in 1 and vice versa as both form and function, where “existence” can be viewed as either form or function depending upon the relativistic point of measurement,

One exists through itself, hence is directed towards itself.

One directed towards itself divides itself as 1 and 1. This self direction results into a division of 1.

This division of 1, through one tending towards 1, results in 2 through the fraction of 1. 1 however maintains itself as 1 considering all division through 1 and extensions of 1 requires 1 in itself to maintain itself as the same.

1 dividing itself results in 2 as it folds through itself. “∢" observes the inherent “number of “1’s”” which compose the fraction as a form of self folding.

The number of divisions exists simultaneously as a negative number as one folding through itself, simultaneously causes itself to negate reducing it back to one. The act of division observes an act of negation and in these respects stems from deficiency through subtraction.

Folding acts as the quantification of quantification in which the number line manifests through itself as a form of alternation.

Folding it 1 tending towards itself resulting in an inherent multiplicity through the manifestation of fractals.

The folding of a fraction results in an inherent multiplicity where the resulting numbers are 1 in themselves hence multiples of 1.

(1/1 ∢ 1(+2,-1)) → ((1/1)/1 ∢ 1(+3,-2)) → (((1/1)/1)/1 ∢ 1(+4,-3))→ ((((1/1)/1)/1)/1 ∢ 1(+5,-4))→⋯.

Fractions can be observed as:

1→(1→1)→(1 →1→1)→(1→1→1→1)→(1→1→1→1→1)…

1→((((1→1)→1)→1))→1) →⋯.

1 progresses to 2 through self division, with 2 (as 1 dividing itself) dividing 1 as 3, etc. All acts of 1 dividing itself through fractals results in whole numbers.

1 as self-dividing, maintains this division ad-infinitum, hence 1 tends towards infinity as 1.

1 as self dividing, forms 1 as its own boundary through division and in these respects 1 exists as infinite division.

1 exists as infinite change through itself with 1 existing as division in itself. This division is a result of 1 tending towards itself as its own predicate to maintain its existence.

Considering the files I want to attach cannot be attached to show the number line, here is a link to another forum with the file attached at bottom:

http://arktos.boards.net/thread/2670/fo ... umber-line

## Folding Function as Function for Number Line

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