Line 8,023: |
Line 8,023: |
| o------o-------------------------o-----------------------------------------------o | | o------o-------------------------o-----------------------------------------------o |
| </pre> | | </pre> |
| + | |
| + | {| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; text-align:left; width:96%" |
| + | |+ '''Table 54. Cast of Characters: Expansive Subtypes of Objects and Operators''' |
| + | |- style="background:paleturquoise" |
| + | ! Item |
| + | ! Notation |
| + | ! Description |
| + | ! Type |
| + | |- |
| + | | ''U''<sup> •</sup> |
| + | | = [''u'', ''v''] |
| + | | Source Universe |
| + | | ['''B'''<sup>2</sup>] |
| + | |- |
| + | | ''X''<sup> •</sup> |
| + | | = [''x''] |
| + | | Target Universe |
| + | | ['''B'''<sup>1</sup>] |
| + | |- |
| + | | E''U''<sup> •</sup> |
| + | | = [''u'', ''v'', d''u'', d''v''] |
| + | | Extended Source Universe |
| + | | ['''B'''<sup>2</sup> × '''D'''<sup>2</sup>] |
| + | |- |
| + | | E''X''<sup> •</sup> |
| + | | = [''x'', d''x''] |
| + | | Extended Target Universe |
| + | | ['''B'''<sup>1</sup> × '''D'''<sup>1</sup>] |
| + | |- |
| + | | ''J'' |
| + | | ''J'' : ''U'' → '''B''' |
| + | | Proposition |
| + | | ('''B'''<sup>2</sup> → '''B''') ∈ ['''B'''<sup>2</sup>] |
| + | |- |
| + | | ''J'' |
| + | | ''J'' : ''U''<sup> •</sup> → ''X''<sup> •</sup> |
| + | | Transformation, or Mapping |
| + | | ['''B'''<sup>2</sup>] → ['''B'''<sup>1</sup>] |
| + | |- |
| + | | valign="top" | |
| + | {| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%" |
| + | | W |
| + | |} |
| + | | valign="top" | |
| + | {| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%" |
| + | | W : |
| + | |- |
| + | | ''U''<sup> •</sup> → E''U''<sup> •</sup> , |
| + | |- |
| + | | ''X''<sup> •</sup> → E''X''<sup> •</sup> , |
| + | |- |
| + | | (''U''<sup> •</sup> → ''X''<sup> •</sup>) |
| + | |- |
| + | | → |
| + | |- |
| + | | (E''U''<sup> •</sup> → E''X''<sup> •</sup>) , |
| + | |- |
| + | | for each W in the set: |
| + | |- |
| + | | {<math>\epsilon</math>, <math>\eta</math>, E, D, d} |
| + | |} |
| + | | valign="top" | |
| + | {| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%" |
| + | | Operator |
| + | |} |
| + | | valign="top" | |
| + | {| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100" |
| + | | |
| + | |- |
| + | | ['''B'''<sup>2</sup>] → ['''B'''<sup>2</sup> × '''D'''<sup>2</sup>] , |
| + | |- |
| + | | ['''B'''<sup>1</sup>] → ['''B'''<sup>1</sup> × '''D'''<sup>1</sup>] , |
| + | |- |
| + | | (['''B'''<sup>2</sup>] → ['''B'''<sup>1</sup>]) |
| + | |- |
| + | | → |
| + | |- |
| + | | (['''B'''<sup>2</sup> × '''D'''<sup>2</sup>] → ['''B'''<sup>1</sup> × '''D'''<sup>1</sup>]) |
| + | |- |
| + | | |
| + | |- |
| + | | |
| + | |} |
| + | |- |
| + | | |
| + | {| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%" |
| + | | <math>\epsilon</math> |
| + | |- |
| + | | <math>\eta</math> |
| + | |- |
| + | | E |
| + | |- |
| + | | D |
| + | |- |
| + | | d |
| + | |} |
| + | | valign="top" | |
| + | | colspan="2" | |
| + | {| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:60%" |
| + | | Tacit Extension Operator || <math>\epsilon</math> |
| + | |- |
| + | | Trope Extension Operator || <math>\eta</math> |
| + | |- |
| + | | Enlargement Operator || E |
| + | |- |
| + | | Difference Operator || D |
| + | |- |
| + | | Differential Operator || d |
| + | |} |
| + | |- |
| + | | valign="top" | |
| + | {| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%" |
| + | | <font face=georgia>'''W'''</font> |
| + | |} |
| + | | valign="top" | |
| + | {| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%" |
| + | | <font face=georgia>'''W'''</font> : |
| + | |- |
| + | | ''U''<sup> •</sup> → <font face=georgia>'''T'''</font>''U''<sup> •</sup> = E''U''<sup> •</sup> , |
| + | |- |
| + | | ''X''<sup> •</sup> → <font face=georgia>'''T'''</font>''X''<sup> •</sup> = E''X''<sup> •</sup> , |
| + | |- |
| + | | (''U''<sup> •</sup> → ''X''<sup> •</sup>) |
| + | |- |
| + | | → |
| + | |- |
| + | | (<font face=georgia>'''T'''</font>''U''<sup> •</sup> → <font face=georgia>'''T'''</font>''X''<sup> •</sup>) , |
| + | |- |
| + | | for each <font face=georgia>'''W'''</font> in the set: |
| + | |- |
| + | | {<font face=georgia>'''e'''</font>, <font face=georgia>'''E'''</font>, <font face=georgia>'''D'''</font>, <font face=georgia>'''T'''</font>} |
| + | |} |
| + | | valign="top" | |
| + | {| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%" |
| + | | Operator |
| + | |} |
| + | | valign="top" | |
| + | {| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100" |
| + | | |
| + | |- |
| + | | ['''B'''<sup>2</sup>] → ['''B'''<sup>2</sup> × '''D'''<sup>2</sup>] , |
| + | |- |
| + | | ['''B'''<sup>1</sup>] → ['''B'''<sup>1</sup> × '''D'''<sup>1</sup>] , |
| + | |- |
| + | | (['''B'''<sup>2</sup>] → ['''B'''<sup>1</sup>]) |
| + | |- |
| + | | → |
| + | |- |
| + | | (['''B'''<sup>2</sup> × '''D'''<sup>2</sup>] → ['''B'''<sup>1</sup> × '''D'''<sup>1</sup>]) |
| + | |- |
| + | | |
| + | |- |
| + | | |
| + | |} |
| + | |- |
| + | | |
| + | {| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%" |
| + | | <font face=georgia>'''e'''</font> |
| + | |- |
| + | | <font face=georgia>'''E'''</font> |
| + | |- |
| + | | <font face=georgia>'''D'''</font> |
| + | |- |
| + | | <font face=georgia>'''T'''</font> |
| + | |} |
| + | | valign="top" | |
| + | | colspan="2" | |
| + | {| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:60%" |
| + | | Radius Operator || <font face=georgia>'''e'''</font> = ‹<math>\epsilon</math>, <math>\eta</math>› |
| + | |- |
| + | | Secant Operator || <font face=georgia>'''E'''</font> = ‹<math>\epsilon</math>, E› |
| + | |- |
| + | | Chord Operator || <font face=georgia>'''D'''</font> = ‹<math>\epsilon</math>, D› |
| + | |- |
| + | | Tangent Functor || <font face=georgia>'''T'''</font> = ‹<math>\epsilon</math>, d› |
| + | |} |
| + | |}<br> |
| | | |
| ===Table 59. Synopsis of Terminology: Restrictive and Alternative Subtypes=== | | ===Table 59. Synopsis of Terminology: Restrictive and Alternative Subtypes=== |