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Revision as of 02:44, 2 July 2007

1,489 bytes removed ,  02:44, 2 July 2007
→‎Table 58. Cast of Characters: Expansive Subtypes of Objects and Operators
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| ['''B'''<sup>2</sup>] &rarr; ['''B'''<sup>2</sup> &times; '''D'''<sup>2</sup>]&nbsp;,
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| ['''B'''<sup>''n''</sup>] &rarr; ['''B'''<sup>''n''</sup> &times; '''D'''<sup>''n''</sup>]&nbsp;,
 
|-
 
|-
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| ['''B'''<sup>1</sup>] &rarr; ['''B'''<sup>1</sup> &times; '''D'''<sup>1</sup>]&nbsp;,
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| ['''B'''<sup>''k''</sup>] &rarr; ['''B'''<sup>''k''</sup> &times; '''D'''<sup>''k''</sup>]&nbsp;,
 
|-
 
|-
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| (['''B'''<sup>2</sup>] &rarr; ['''B'''<sup>1</sup>])
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| (['''B'''<sup>''n''</sup>] &rarr; ['''B'''<sup>''k''</sup>])
 
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|-
 
| &rarr;
 
| &rarr;
 
|-
 
|-
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| (['''B'''<sup>2</sup> &times; '''D'''<sup>2</sup>] &rarr; ['''B'''<sup>1</sup> &times; '''D'''<sup>1</sup>])
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| (['''B'''<sup>''n''</sup> &times; '''D'''<sup>''n''</sup>] &rarr; ['''B'''<sup>''k''</sup> &times; '''D'''<sup>''k''</sup>])
 
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|-
 
| &nbsp;
 
| &nbsp;
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<pre>
  −
-------------o
  −
| W    | W :                    | Operator        |                            |
  −
|      | U% -> EU%,              |                  | [B^n] -> [B^n x D^n],      |
  −
|      | X% -> EX%,              |                  | [B^k] -> [B^k x D^k],      |
  −
|      | (U%->X%)->(EU%->EX%),  |                  | ([B^n] -> [B^k])          |
  −
|      | for each W among:      |                  | ->                        |
  −
|      | !e!, !h!, E, D, d      |                  | ([B^n x D^n]->[B^k x D^k]) |
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-------------o
  −
| !e!  |  | Tacit Extension Operator  !e!
  −
| !h!  |  | Trope Extension Operator  !h!
  −
|  E  |  | Enlargement Operator        E
  −
|  D  |  | Difference Operator        D
  −
|  d  |  | Differential Operator      d
  −
-------------o
  −
| $W$  | $W$ :          | Operator        |                            |
  −
|      | U% -> $T$U% = EU%,      |                  | [B^n] -> [B^n x D^n],      |
  −
|      | X% -> $T$X% = EX%,      |                  | [B^k] -> [B^k x D^k],      |
  −
|      | (U%->X%)->($T$U%->$T$X%)|                  | ([B^n] -> [B^k])          |
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|      | for each $W$ among:    |                  | ->                        |
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|      | $e$, $E$, $D$, $T$      |                  | ([B^n x D^n]->[B^k x D^k]) |
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-------------o
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| $e$  |  | Radius Operator        $e$  =  <!e!, !h!>    |
  −
| $E$  |  | Secant Operator        $E$  =  <!e!,  E >    |
  −
| $D$  |  | Chord Operator        $D$  =  <!e!,  D >    |
  −
| $T$  |  | Tangent Functor        $T$  =  <!e!,  d >    |
  −
-------------o
  −
</pre>
      
===Table 59.  Synopsis of Terminology:  Restrictive and Alternative Subtypes===
 
===Table 59.  Synopsis of Terminology:  Restrictive and Alternative Subtypes===
Jon Awbrey
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