# 8. Parallel Numbers Postulate

## — Eumetry of Paradox; Zerometry —

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The Number Line

The Unified Line

We think of a number line like this:

… +3…+2…+1…±0…–1… –2… –3…

Each number on this line an integer, in their midst *Zero*, central among numbers. We see every positive number has a negative number that parallels it, meaning Zero is his-her own parallel. (A geometrical analogue to zero could be the point and all forms considered analogue to it, each a parallel of any other; the point parallel the circle parallel the sphere.)

Parallel Numbers

Re-considering number as a set of parallels, we could think of the number line like parallel lines, in which case they would be given like this:

ⓩ… +1 … +2 … +3 …

ⓩ… –1 … –2 … –3 …

Re-presenting the number line in this way we need to find a non-numerical symbol for Zero as *Ze* — *unity* generalized — is always one and cannot be considered as *either* plus or minus, always and everywhere being exactly both. Just like Zero. It’s Platonic.

A-positive and A-negative are distinctly different, radically opposed entities, standing for uniquely non-same ideas, yet in this also being identical in the only way identity is possible in a non-trivial sense.

Re-thinking these integers as not generic integers — cardinal integers representing only themselves — but *ordinal* integers, each embodying an identity, the positive one corresponding to a negative one and vice versa, each denoting simultaneously a defined and limited area of definition and its precise, radical, opposite. An example might clarify: If a positive amount of apples equates ‘2 apples’, the corresponding negative ordinal integer gives *exactly *everything else everywhere, eternally. Identical universe minus two apples.

Re-formulating positive-negative in such terms retains the one-to-one correspondence, but provides us with a way in which we can view this correspondence as an identity and a radical opposition at the same time. It does not change the universe, but it might give a way to try out different scenarios.

We may also rethink the number line into a parallel consisting not only of Platonic Zero and Platonic One, but with every number upon it-them “Platonic”. Such a parallelism could be understood in several ways, below a duo of doubles.

Diophantic Parallels

*Nominative*. Positive numbers equal 1 times n.*Denominative*. Negative numbers equal 1 through n.*Additive*. Positive numbers equal 1 + n.*Subtractive*. Negative numbers equal 1 - n.

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