ONT Re: Relations And Their Divisitudes
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RATD. Note 12
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Pursuing the course of this geometric vein,
let us now return to the 3-adic relation L
that is given by this aggregate of triples:
<a, b, c>
<a, b, d>
<a, c, d>
Figure 2 shows the 3-adic relation L as a geometric configuration
embedded in the 3-dimensional space X = X_1 x X_2 x X_3 ~=~ !A!^3,
rendered here in 3-dimensional perspective drawing.
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| |
| X_3 |
| |
| d |
| / \ |
| / \ |
| . \ |
| /|\ \ |
| / | \ \ |
| / . \ . |
| / |\ \ / \ |
| / | \ \ / \ |
| / | \ y . |
| / | \ |\ /|\ |
| / | \| \ / | \ |
| o | x z . o |
| | | |\ | /| | |
| | | | \|/ | | |
| | a | . | | |
| | / \ | | | | |
| | / \ | | | | |
| | b \ | | | | |
| | / \ | | | | |
| | / \| | | | |
| | c <a,b> . | c | |
| | / \ | / \ | |
| |/ \|/ \| |
| d <a,c> . d |
| X_1 \ / X_2 |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| \ / |
| Relation L: \ / |
| \ / |
| x = <a,b,c> \ / |
| y = <a,b,d> \ / |
| z = <a,c,d> o |
| |
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Figure 2. Relation L in 3-Dimensional Perspective
Jon Awbrey
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