Dependency of set existence to set members

If one (1) number ceased to exist in the total set of infinity of numbers then
the total set would cease to exist

Set patterns

All sets are specialized and unique to some degree
All sets are co-dependent to some degree
All sets are similar to some degree and relationships of real world objects.

GEOLEX

The laws of GEOLEX and existence state:

Points

A number may be described as point in two (2) or three (3) dimensional
space.
No two (2) points may ever occupy the same position.
A point is uniquely aware of its position in dimension.
Points can only interact with immediate neighbour points.

Construct

All relationships between two (2) or more points create geometric patterns
in two (2) and three (3) dimensional space called constructs possessing
common and unique properties.

Path

A shape made from the analysis of the past, present or future position of
points are called paths.
All paths may be defined by type of motion and themselves have common
and unique properties.

Morphology

All geometric constructs change shape to some degree when in motion
along a particular path. This change from one (1) shape to another is called
a morph track.

Frame

The rate of time measure of change from one (1) place on a path or morph
to another is called a frame. A collection of measured time changes is
called frameset.

Model

The combination of a construct and a path or morph track to a frameset is
called a model. The existence of a construct in relation to a model is called
an instance.

System

The combination of more than one (1) model interacting together is called a
system having common and unique properties / behaviour.

SYMERICS

The laws of SYMERICS and existence state:

Variable

All known types of logos, numerics and Geolex may be represented as
unique sets of theoretical symbols representing possible values called
variables.
All variables are specialized and unique to some degree (unique variables).
All variables are co-dependent to some degree (co-dependent variables).
All variables are common and interchangeable to some degree (universal
variables).

Formula

All geometric models, systems and number patterns may be expressed as
formulas of variables.
All variables contained within a formula must be defined by their type
(unique, co-dependent or universal) and type.
For a formula to function properly, the correct substitution of variables by
type and purpose must take place.

Formula type

The function of a formula (in terms of structure and flow of variables) may
be expressed as linear, matrix or multi-dimensional types.
The utility and scope of a formula to describe theoretical and real is limited
by its type (linear, matrix, multi-dimensional).

AXIOMATICS

The laws of AXIOMATICS and existence state:

Axiom

All ideas may be stated as axioms based on functional symeric formulas
themselves based on assumptions.
All axioms may themselves be described as a process of inputs inserted
into a function to produce an output.

Axiom utility

The utility of an axiom is relative to the purpose and function it is used.
An axiom that balances inputs to output according to purpose is in harmony
(harmonic axiom).
An axiom that produces less output to input according to purpose is in
decay (dissonant axiom).
An axiom that produces more output to input according to purpose is in
growth (dynamic axiom).

Axiomatic proof

The proof of an axiom is relative to the purpose and function it is used.
An axiom that adheres to the rules of EIKOS in its construction and use is
true and proof itself. An axiom that does not adhere to the rules of EIKOS is
false and unprovable.
Mathematical rules of proof may not be applied as test of axiomatic proof.
Only true axioms may be used as proof relative to EIKOS and the UCADIAN
model of knowledge.

Complexity and axioms

Complex axiom resolve themselves to describe only simple systems.
Simple axiom resolve themselves to describe both simple and complex
systems.

KINESIS

The laws of KINESIS (motion) and existence state:

Kinesis

All objects in motion may be expressed in Kinesis - higher axiomatics
Simple axiom resolve themselves to describe both simple and complex
systems.
Kinesis is the description and understanding of motion.
There are only three (3) types of kinesis (motion) kinetic, structural and
harmonic. - Kinetic is motion in form expressed as the free velocity of an
object; - Structural.kinesis is motion in form expressed as the structural
association with other like and larger objects; - Harmonic.kinesis is motion
within form expressed as vibration and spin.

Simple kinetic axioms

All objects in motion may be expressed in Kinesis - higher axiomatics
Simple axiom resolve themselves to describe both simple and complex
systems.

Motion

Existence is awareness (UCA) in motion
Existence is awareness in motion (as form) in motion.
Existence is specialized motion (structural as form), (harmonic as vibration
in form) and velocity (movement in form).
All motion is relative. The total motion of an object is relative to its type and
structural relationships.
All motion of an object is conserved. An object may not travel faster than its
fastest rate.
All motion is relative.
All motion is unique.
All motion is similar in terms of common types of objects and patterns of
motion.

Paradox of motion

The sum of the whole motion of a form is greater than the parts that make
it.

Property of motion

All objects share the property of motion and share common characteristics
inherited from the smallest particles that create the form.

Energis

Energis is the measure of aggregated motion of all particles in motion to
create mass (accumulative kinesis).
There are only three (3) types of energis (motion) kinetic, structural and
harmonic. - Kinetic is motion in form expressed as the free velocity of an
object; - Structural.energis is motion in form expressed as the structural
association with other like and larger objects; - Harmonic.energis is motion
within form expressed as vibration and spin.

Mass

Mass is equal to the number of benchmark objects by their like
accumulative Kinesis (kinetic, structural and harmonic).
The greater the geometric structural integrity (harmony) of benchmark
objects, the greater structural kinesis, the greater the mass, the greater its
energis.
Mass is a measure of the tendency of a body (of objects) to resist changes
(dissonance) in its state of kinetic and harmonic motion.
All individual objects smaller than or equal to up-quarks that are not up-
quarks have no measurable mass.
This boundary exists and is the kinetic-mass boundary.

Force

No independent non-object exists within the universe capable of physically
influencing matter. Only matter can influence matter. No forces exist.
All phenomena observed as the apparent interaction of forces is the
exclusive interaction of only matter, its attributes and motion.
A fortis is an aggregate feature of all structures of matter that has the
capacity to produce a change in another structure behaviour, in terms of
make-up and rate of motion. A unit of measured fortis is called an ergo.
All objects of matter possess three (3) fortis in varying degrees of strength
derived from each and every Unita possessing self-awareness of form:
Creation - all matter wishes to create greater (and therefore more
complex) form; Attraction - all matter has relative attractiveness to other
forms of matter by virtue of the spin configuration of its smallest pieces of
matter, built up to an aggregate spin;
Repulsion - all matter has relative repulsiveness to other forms of matter by
virtue of the spin configuration of its smallest pieces of matter, built up to
an aggregate spin;
Fortis of harmonic attraction
Matter vibrating in unison, or harmonic ratio, is mutually attracted to forming
closer bonds.