CLOSED LOOP INTERVAL ONTOLOGY
       The Digital Integration of Conceptual Form
TzimTzum/Kaballah | Loop definition | Home | ORIGIN    
Please sign in
or register

Email *

Password *

Home | About

Select display
Show public menu
Show all theme groups
Show all themes
Show all terms
Order results by
Alphabetical
Most recently edited
Progress level
Placeholder
Note
Sketch
Draft
Polished


Searches selected display

The Many Forms of Many/One
Universal conceptual form

Invocation
Aligning the vision

Project under development
Evolving and coalescing

Guiding motivation
Why we do this

A comprehensive vision
Ethics / governance / science

Cybernetic democracy
Homeostatic governance

Collective discernment
Idealized democracy

Objectives and strategy
Reconciliation and integration

Reconciliation of perspectives
Holistic view on alternatives

What is a concept?
Definitions and alternatives

Theories of concepts
Compare alternatives

What is truth?
How do we know?

Semantics
How meaning is created

Synthetic dimensionality
Foundational recursive definition

Universal hierarchy
Spectrum of levels

A universal foundation
The closed loop ensemble contains
all primary definitions

Set
Dimensions of set theory

Numbers
What is a number?

Venn diagrams
Topology of sets

Objects in Boolean algebra
How are they constructed?

Core vocabulary
Primary terms

Core terms on the strip
Closed Loop framework

Graphics
Hierarchical models

Digital geometry
Euclid in digital space

The dimensional construction
of abstract objects
Foundational method

The digital integration
of conceptual form
Compositional semantics

Closed loop interval ontology
How it works

Cognitive science
The integrated science of mind

Equality
What does it mean?

Formal systematic definitions
Core terms

Data structures
Constructive elements
and building blocks

Compactification
Preserving data under transformation

Steady-state cosmology
In the beginning

Semantic ontology
Domain and universal

Foundational ontology
A design proposal

Coordinate systems
Mapping the grid

Articles
From other sources

Arithmetic
Foundational computation

Plato's republic and
homeostatic democracy
Perfecting political balance

Branching computational architecture
Simultaneity or sequence

Abstract math and HTML
Concrete symbolic representation

All knowledge as conceptual
Science, philosophy and math
are defined in concepts

Does the Closed Loop
have an origin?
Emerging from a point


Theme
Ordered set
Placeholder

Definition / description

In mathematics, a total order, simple order,[1] linear order, connex order,[2] or full order[3] is a binary relation on some set {\displaystyle X}X, which is antisymmetric, transitive, and a connex relation. A set paired with a total order is called a chain,[4] a totally ordered set,[4] a simply ordered set,[1] a linearly ordered set,[2][4] or a loset.[5][6]

Formally, a binary relation {\displaystyle \leq }\leq is a total order on a set {\displaystyle X}X if the following statements hold for all {\displaystyle a,b}a,b and {\displaystyle c}c in {\displaystyle X}X:

Antisymmetry: If {\displaystyle a\leq b}a\leq b and {\displaystyle b\leq a}{\displaystyle b\leq a} then {\displaystyle a=b}a=b; Transitivity: If {\displaystyle a\leq b}a\leq b and {\displaystyle b\leq c}{\displaystyle b\leq c} then {\displaystyle a\leq c}{\displaystyle a\leq c}; Connexity: {\displaystyle a\leq b}a\leq b or {\displaystyle b\leq a}{\displaystyle b\leq a}.

Antisymmetry eliminates uncertain cases when both {\displaystyle a}a precedes {\displaystyle b}b and {\displaystyle b}b precedes {\displaystyle a}a.[7]:325 A relation having the connex property means that any pair of elements in the set of the relation are comparable under the relation. This also means that the set can be diagrammed as a line of elements, giving it the name linear.[7]:330 The connex property also implies reflexivity, i.e., a ? a. Therefore, a total order is also a (special case of a) partial order, as, for a partial order, the connex property is replaced by the weaker reflexivity property. An extension of a given partial order to a total order is called a linear extension of that partial order.

Hide Placeholder Note Sketch Draft Polished

Sat, Mar 20, 2021