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→Table 58. Cast of Characters: Expansive Subtypes of Objects and Operators
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|+ '''Table 54. Cast of Characters: Expansive Subtypes of Objects and Operators'''
|+ '''Table 58. Cast of Characters: Expansive Subtypes of Objects and Operators'''
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! Item
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<pre>
| U% | = [u, v] | Source Universe | [B^n] |
| | | | |
-------------o
| | | | |
| X% | = [x, y] | Target Universe | [B^k] |
| | = [f, g] | | |
| | | | |
-------------o
| | | | |
| EU% | = [u, v, du, dv] | Extended | [B^n x D^n] |
| | | Source Universe | |
| | | | |
-------------o
| | | | |
| EX% | = [x, y, dx, dy] | Extended | [B^k x D^k] |
| | = [f, g, df, dg] | Target Universe | |
| | | | |
-------------o
| | | | |
| F | F = <f, g> : U% -> X% | Transformation, | [B^n] -> [B^k] |
| | | or Mapping | |
| | | | |
-------------o
| | | | |
| | f, g : U -> B | Proposition, | B^n -> B |
| | | special case | |
| f | f : U -> [x] c X% | of a mapping, | c (B^n, B^n -> B) |
| | | or component | |
| g | g : U -> [y] c X% | of a mapping. | = (B^n +-> B) = [B^n] |
| | | | |
-------------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]) |
| | | | |
-------------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]) |
| | for each $W$ among: | | -> |
| | $e$, $E$, $D$, $T$ | | ([B^n x D^n]->[B^k x D^k]) |
| | | | |
-------------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
</pre>
===Table 59. Synopsis of Terminology: Restrictive and Alternative Subtypes===
===Table 59. Synopsis of Terminology: Restrictive and Alternative Subtypes===