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| </pre> | | </pre> |
| | | |
− | ===Table 54. Cast of Characters: Expansive Subtypes of Objects and Operators=== | + | ===Table 54. Cast of Characters: Expansive Subtypes of Objects and Operators=== |
| | | |
| <pre> | | <pre> |
Line 6,413: |
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| | | |
| <pre> | | <pre> |
− | o------o-------------------------o------------------o----------------------------o
| + | |
− | | Item | Notation | Description | Type |
| + | | U% | = [u, v] | Source Universe | [B^2] |
− | o------o-------------------------o------------------o----------------------------o
| + | |
− | | | | | |
| + | -------------o |
− | | U% | = [u, v] | Source Universe | [B^2] | | + | |
− | | | | | |
| + | | X% | = [x] | Target Universe | [B^1] |
− | o------o-------------------------o------------------o----------------------------o
| + | |
− | | | | | |
| + | -------------o |
− | | X% | = [x] | Target Universe | [B^1] | | + | |
− | | | | | |
| + | | EU% | = [u, v, du, dv] | Extended Source Universe | [B^2 x D^2] |
− | o------o-------------------------o------------------o----------------------------o
| + | |
− | | | | | |
| + | -------------o |
− | | EU% | = [u, v, du, dv] | Extended | [B^2 x D^2] | | + | |
− | | | | Source Universe | |
| + | | EX% | = [x, dx] | Extended Target Universe | [B^1 x D^1] |
− | | | | | |
| + | |
− | o------o-------------------------o------------------o----------------------------o
| + | -------------o |
− | | | | | |
| + | |
− | | EX% | = [x, dx] | Extended | [B^1 x D^1] | | + | | J | J : U -> B | Proposition | (B^2 -> B) c [B^2] |
− | | | | Target Universe | |
| + | |
− | | | | | |
| + | -------------o |
− | o------o-------------------------o------------------o----------------------------o
| + | |
− | | | | | |
| + | | J | J : U% -> X% | Transformation, or Mapping | [B^2] -> [B^1] |
− | | J | J : U -> B | Proposition | (B^2 -> B) c [B^2] | | + | |
− | | | | | |
| + | -------------o |
− | o------o-------------------------o------------------o----------------------------o
| + | |
− | | | | | |
| + | | W | W : | Operator |
− | | J | J : U% -> X% | Transformation, | [B^2] -> [B^1] | | + | |
− | | | | or Mapping | |
| + | | | U% -> EU%, | | [B^2] -> [B^2 x D^2], |
− | | | | | |
| + | |
− | o------o-------------------------o------------------o----------------------------o
| + | | | X% -> EX%, | | [B^1] -> [B^1 x D^1], |
− | | | | | |
| + | |
− | | W | W : | Operator | | | + | | | (U%->X%)->(EU%->EX%), | | ([B^2] -> [B^1]) |
− | | | U% -> EU%, | | [B^2] -> [B^2 x D^2], | | + | |
− | | | X% -> EX%, | | [B^1] -> [B^1 x D^1], | | + | | | for each W among: | | -> |
− | | | (U%->X%)->(EU%->EX%), | | ([B^2] -> [B^1]) | | + | | | e!, !h!, E, D, d | | ([B^2 x D^2]->[B^1 x D^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----------------------------o
| + | | !e! | | Tacit Extension Operator !e! |
− | | | | |
| + | | !h! | | Trope Extension Operator !h! |
− | | !e! | | Tacit Extension Operator !e! | | + | | E | | Enlargement Operator E |
− | | !h! | | Trope Extension Operator !h! | | + | | D | | Difference Operator D |
− | | E | | Enlargement Operator E | | + | | d | | Differential Operator d |
− | | D | | Difference Operator D | | + | |
− | | d | | Differential Operator d | | + | -------------o |
− | | | | |
| + | |
− | o------o-------------------------o------------------o----------------------------o
| + | | $W$ | $W$ : | Operator |
− | | | | | |
| + | |
− | | $W$ | $W$ : | Operator | | | + | | | U% -> $T$U% = EU%, | | [B^2] -> [B^2 x D^2], |
− | | | U% -> $T$U% = EU%, | | [B^2] -> [B^2 x D^2], | | + | |
− | | | X% -> $T$X% = EX%, | | [B^1] -> [B^1 x D^1], | | + | | | 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: | | -> | | + | | | (U%->X%)->($T$U%->$T$X%)| | ([B^2] -> [B^1]) |
− | | | $e$, $E$, $D$, $T$ | | ([B^2 x D^2]->[B^1 x D^1]) | | + | |
− | | | | | |
| + | | | for each $W$ among: | | -> |
− | o------o-------------------------o------------------o----------------------------o
| + | |
− | | | | |
| + | | | $e$, $E$, $D$, $T$ | | ([B^2 x D^2]->[B^1 x D^1]) |
− | | $e$ | | Radius Operator $e$ = <!e!, !h!> | | + | |
− | | $E$ | | Secant Operator $E$ = <!e!, E > | | + | -------------o |
− | | $D$ | | Chord Operator $D$ = <!e!, D > | | + | |
− | | $T$ | | Tangent Functor $T$ = <!e!, d > | | + | | $e$ || Radius Operator $e$ = <!e!, !h!> |
− | | | | |
| + | | $E$ || Secant Operator $E$ = <!e!, E > |
− | o------o-------------------------o-----------------------------------------------o
| + | | $D$ || Chord Operator $D$ = <!e!, D > |
| + | | $T$ || Tangent Functor $T$ = <!e!, d > |
| + | |
| + | -------------o |
| </pre> | | </pre> |
| | | |