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Unnamed Structures 1: Axioms

2023-01-12 | tags : structure | axiomatics
An ensemble of complexes

There exist a system made of units (.) and bonds (-). Units do not exist in isolation, they can only exist in a bond with one or more units.

Although a graphical representation of these structures can be given, the structures themselves are dimensionless.

  • I. Units cannot occupy the same space
  • II. Only one bond is possible between any two units
  • III. A unit can have an unlimited number of bonds
  • IV. Units exist only if linked by a bond
  • V. Bonds exist only if linked to two units

Minimal element

From [II] and [IV] we derive that the minimal element possible is composed of two units linked by a single bond.

Maximal element

The maximal element has an infinite number of units and an infinite number of bonds. what is known from [III] is that the infinite element is a unit - i.e. there cannot be a bond without a unit. Also we know that there are as twice as many bonds in any element.

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