A Simple Set

As we have seen, it becomes clearly evident that two different types of nodes appear in our exploration: $set$ and $concept$.

Let’s call $S$ the set of all $sets$:

$\{se{t}_1,se{t}_2,se{t}_3,...\}=S$

And $C$ the set of all $concepts$:

$\{concep{t}_1,concep{t}_2,concep{t}_3,...\}=C$

In the rest of this document, we will call $item$ any $set$ or $concept$:

$item=\{\begin{array}{l}set\in S\\ \text{or}\\ concept\in C\end{array}$

We could say that:

${\bigcup }_{k}ite{m}_k=I=S\cup C$

Sets

$Sets$ contain $items$ (mostly $concepts$ and sometimes other $sets$) and represent a form of hierarchy. For example for a given $se{t}_{\mu }$, we have:

$ite{m}_1,ite{m}_2,ite{m}_3,...\in se{t}_{\mu }$

and then can be represented by a graph:

We can build a simple hierarchical (H) relationship between the set and its items:

$\{\begin{array}{l}se{t}_{\mu }\to ite{m}_1\\ se{t}_{\mu }\to ite{m}_2\\ se{t}_{\mu }\to ite{m}_3\\ ...\end{array}$

$\text{or}$

$se{t}_{\mu }\stackrel{H}{\to }item{s}_{\mu }$

Concepts

$Concepts$ relates (R) to other $items$ in a similar way. For a given $concep{t}_{\nu }$, we have:

$concep{t}_{\nu }\stackrel{R}{\to }item{s}_{\nu }$

This will help establish a simple network of connectivity based on those relationships of H and R types.

we could consider also the relationship R between sets but it is quite rare (ex: 8path 3train) and is linked via concept anyway at a higher degree.

Notation

To keep thing easy to identify, we will always start the names of $sets$ with a digit.

For example, the set $3Cravings$ contains 3 items:
“Sensuality”, “Becoming”, “Non-Becoming”

and the concept “Path” relates to items:
“8-Fold Path”, ‘3-Fold Training”, ‘“3 Pillars”, “7 Purifications”

TODO: add exemple that contains both type as child

Note that in common literature, we call items: node or vortex. Edges are their relations (contains or relates).

Two Approches

1. Relationship (for Concepts)

Graph Example: Vertex, edges

2. Hierarchy (for Sets)

Graph Example: Tree like structure, children

Conclusion

We have to deal with a mix.