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===Table 54. Cast of Characters: Expansive Subtypes of Objects and Operators===
===Table 54. Cast of Characters: Expansive Subtypes of Objects and Operators===
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o------o-------------------------o-----------------------------------------------o
o------o-------------------------o-----------------------------------------------o
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<font face=georgia>'''W'''</font>
<font face="courier new">
<font face="courier new">
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; text-align:left; width:96%"
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; text-align:left; width:96%"
|+ '''Table 2. Fundamental Notations for Propositional Calculus'''
|+ '''Table 54. Cast of Characters: Expansive Subtypes of Objects and Operators'''
|- style="background:paleturquoise"
|- style="background:paleturquoise"
! Symbol
! Item
! Notation
! Notation
! Description
! Description
['''B'''<sup>''n''</sup>]
['''B'''<sup>''n''</sup>]
|}</font><br>
|}</font><br>
<pre>
o------o-------------------------o------------------o----------------------------o
| Item | Notation | Description | Type |
o------o-------------------------o------------------o----------------------------o
| | | | |
| U% | = [u, v] | Source Universe | [B^2] |
| | | | |
o------o-------------------------o------------------o----------------------------o
| | | | |
| X% | = [x] | Target Universe | [B^1] |
| | | | |
o------o-------------------------o------------------o----------------------------o
| | | | |
| EU% | = [u, v, du, dv] | Extended | [B^2 x D^2] |
| | | Source Universe | |
| | | | |
o------o-------------------------o------------------o----------------------------o
| | | | |
| EX% | = [x, dx] | Extended | [B^1 x D^1] |
| | | Target Universe | |
| | | | |
o------o-------------------------o------------------o----------------------------o
| | | | |
| J | J : U -> B | Proposition | (B^2 -> B) c [B^2] |
| | | | |
o------o-------------------------o------------------o----------------------------o
| | | | |
| J | J : U% -> X% | Transformation, | [B^2] -> [B^1] |
| | | or Mapping | |
| | | | |
o------o-------------------------o------------------o----------------------------o
| | | | |
| W | W : | Operator | |
| | U% -> EU%, | | [B^2] -> [B^2 x D^2], |
| | X% -> EX%, | | [B^1] -> [B^1 x D^1], |
| | (U%->X%)->(EU%->EX%), | | ([B^2] -> [B^1]) |
| | for each W among: | | -> |
| | e!, !h!, E, D, d | | ([B^2 x D^2]->[B^1 x D^1]) |
| | | | |
o------o-------------------------o------------------o----------------------------o
| | | |
| !e! | | Tacit Extension Operator !e! |
| !h! | | Trope Extension Operator !h! |
| E | | Enlargement Operator E |
| D | | Difference Operator D |
| d | | Differential Operator d |
| | | |
o------o-------------------------o------------------o----------------------------o
| | | | |
| $W$ | $W$ : | Operator | |
| | U% -> $T$U% = EU%, | | [B^2] -> [B^2 x D^2], |
| | X% -> $T$X% = EX%, | | [B^1] -> [B^1 x D^1], |
| | (U%->X%)->($T$U%->$T$X%)| | ([B^2] -> [B^1]) |
| | for each $W$ among: | | -> |
| | $e$, $E$, $D$, $T$ | | ([B^2 x D^2]->[B^1 x D^1]) |
| | | | |
o------o-------------------------o------------------o----------------------------o
| | | |
| $e$ | | Radius Operator $e$ = <!e!, !h!> |
| $E$ | | Secant Operator $E$ = <!e!, E > |
| $D$ | | Chord Operator $D$ = <!e!, D > |
| $T$ | | Tangent Functor $T$ = <!e!, d > |
| | | |
o------o-------------------------o-----------------------------------------------o
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===Table 55. Synopsis of Terminology: Restrictive and Alternative Subtypes===
===Table 55. Synopsis of Terminology: Restrictive and Alternative Subtypes===
