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→Quick tour of the neighborhood: rework introduction
==Quick tour of the neighborhood==
==Quick tour of the neighborhood==
This much preparation allows us to present the two most basic axioms of logical graphs, shown in graph and string forms below, along with handy names for referring to the two different directions of applying the axioms.
This much preparation allows us to take up the founding axioms or initial equations that determine the entire system of logical graphs.
===Primary arithmetic as semiotic system===
===Primary arithmetic as semiotic system===
This space of forms, along with the two axioms that induce its [[partition of a set|partition]] into exactly two [[equivalence class]]es, is what [[George Spencer Brown]] called the ''primary arithmetic''.
This space of forms, along with the two axioms that induce its [[partition of a set|partition]] into exactly two [[equivalence class]]es, is what [[George Spencer Brown]] called the ''primary arithmetic''.
The axioms of the primary arithmetic are shown below, as they appear in both graph and string forms, along with pairs of names that come in handy for referring to the opposing directions of applying the axioms.
<pre>
<p>[[Image:Logical_Graph_Figure_14_Banner.jpg|center]]</p>
<br>
<p>[[Image:Logical_Graph_Figure_15_Banner.jpg|center]]</p>
</pre>
<pre>
</pre>
Taking '''S''' to be the set of rooted trees and '''S'''<sub>0</sub> to be the set that has the root node and the rooted edge as its only two elements, writing these facts more briefly as '''S''' = {rooted trees} and '''S'''<sub>0</sub> = {O, |}, simple intuition, or a simple inductive proof, will assure us that any rooted tree can be reduced by means of the axioms of the primary arithmetic either to a root node "@" or else to a rooted edge "|".
Taking '''S''' to be the set of rooted trees and '''S'''<sub>0</sub> to be the set that has the root node and the rooted edge as its only two elements, writing these facts more briefly as '''S''' = {rooted trees} and '''S'''<sub>0</sub> = {O, |}, simple intuition, or a simple inductive proof, will assure us that any rooted tree can be reduced by means of the axioms of the primary arithmetic either to a root node "@" or else to a rooted edge "|".