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| | ['''B'''<sup>2</sup>] → ['''B'''<sup>1</sup>] | | | ['''B'''<sup>2</sup>] → ['''B'''<sup>1</sup>] |
| |- | | |- |
− | | valign="top" | <p>W</p> | + | |- |
− | | valign="top" | <p>W :</p> | + | | valign="top" | |
− | <p>''U''<sup> •</sup> → E''U''<sup> •</sup> ,</p>
| + | {| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%" |
− | <p>''X''<sup> •</sup> → E''X''<sup> •</sup> ,</p>
| + | | W |
− | <p>(''U''<sup> •</sup> → ''X''<sup> •</sup>) →<br>
| + | |} |
− | E''U''<sup> •</sup> → E''X''<sup> •</sup>) ,</p> | + | | valign="top" | |
− | <p>for each W in the set:<br>
| + | {| 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}</p> | + | | W : |
− | | valign="top" | <p>Operator</p> | + | |- |
− | | valign="top" | <p> <p> | + | | ''U''<sup> •</sup> → E''U''<sup> •</sup> , |
− | <p>['''B'''<sup>2</sup>] → ['''B'''<sup>2</sup> × '''D'''<sup>2</sup>] ,</p>
| + | |- |
− | <p>['''B'''<sup>1</sup>] → ['''B'''<sup>1</sup> × '''D'''<sup>1</sup>] ,</p>
| + | | ''X''<sup> •</sup> → E''X''<sup> •</sup> , |
− | <p>(['''B'''<sup>2</sup>] → ['''B'''<sup>1</sup>]) →<br>
| + | |- |
− | (['''B'''<sup>2</sup> × '''D'''<sup>2</sup>] → ['''B'''<sup>1</sup> × '''D'''<sup>1</sup>])</p> | + | | (''U''<sup> •</sup> → ''X''<sup> •</sup>) |
− | <p> <br> </p>
| + | |- |
| + | | → |
| + | |- |
| + | | (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>]) |
| + | |- |
| + | | |
| + | |- |
| + | | |
| + | |} |
| |- | | |- |
| | | | | |
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| |} | | |} |
| |- | | |- |
− | | | + | | |
− | | | + | {| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:100%" |
− | |
| + | | <font face=georgia>'''e'''</font> |
− | | | |
| |- | | |- |
− | | <font face="lucida calligraphy">A<font> | + | | <font face=georgia>'''E'''</font> |
− | | {''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>}
| |
− | | Alphabet
| |
− | | [''n''] = '''n'''
| |
| |- | | |- |
− | | ''A''<sub>''i''</sub> | + | | <font face=georgia>'''D'''</font> |
− | | {(''a''<sub>''i''</sub>), ''a''<sub>''i''</sub>}
| |
− | | Dimension ''i''
| |
− | | '''B'''
| |
| |- | | |- |
− | | ''A'' | + | | <font face=georgia>'''T'''</font> |
− | |
| + | |} |
− | 〈<font face="lucida calligraphy">A</font>〉<br>
| + | | valign="top" | |
− | 〈''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>〉<br>
| + | | colspan="2" | |
− | {‹''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>›}<br> | + | {| align="left" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; text-align:left; width:60%" |
− | ''A''<sub>1</sub> × … × ''A''<sub>''n''</sub><br> | + | | Radius Operator || <font face=georgia>'''e'''</font> = ‹<math>\epsilon</math>, <math>\eta</math>› |
− | ∏<sub>''i''</sub> ''A''<sub>''i''</sub> | |
− | |
| |
− | Set of cells,<br>
| |
− | coordinate tuples,<br>
| |
− | points, or vectors<br>
| |
− | in the universe<br>
| |
− | of discourse
| |
− | | '''B'''<sup>''n''</sup>
| |
| |- | | |- |
− | | ''A''* | + | | Secant Operator || <font face=georgia>'''E'''</font> = ‹<math>\epsilon</math>, E› |
− | | (hom : ''A'' → '''B''') | |
− | | Linear functions | |
− | | ('''B'''<sup>''n''</sup>)* = '''B'''<sup>''n''</sup>
| |
| |- | | |- |
− | | ''A''^ | + | | Chord Operator || <font face=georgia>'''D'''</font> = ‹<math>\epsilon</math>, D› |
− | | (''A'' → '''B''')
| |
− | | Boolean functions
| |
− | | '''B'''<sup>''n''</sup> → '''B'''
| |
| |- | | |- |
− | | ''A''<sup>•</sup> | + | | Tangent Functor || <font face=georgia>'''T'''</font> = ‹<math>\epsilon</math>, d› |
− | | | + | |} |
− | [<font face="lucida calligraphy">A</font>]<br>
| |
− | (''A'', ''A''^)<br>
| |
− | (''A'' +→ '''B''')<br>
| |
− | (''A'', (''A'' → '''B'''))<br>
| |
− | [''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>]
| |
− | | | |
− | Universe of discourse<br>
| |
− | based on the features<br>
| |
− | {''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>}
| |
− | |
| |
− | ('''B'''<sup>''n''</sup>, ('''B'''<sup>''n''</sup> → '''B'''))<br>
| |
− | ('''B'''<sup>''n''</sup> +→ '''B''')<br>
| |
− | ['''B'''<sup>''n''</sup>]
| |
| |}<br> | | |}<br> |
− |
| |
− | <pre>
| |
− | | $e$ || Radius Operator $e$ = <!e!, !h!>
| |
− | | $E$ || Secant Operator $E$ = <!e!, E >
| |
− | | $D$ || Chord Operator $D$ = <!e!, D >
| |
− | | $T$ || Tangent Functor $T$ = <!e!, d >
| |
− | </pre>
| |
| | | |
| ===Table 55. Synopsis of Terminology: Restrictive and Alternative Subtypes=== | | ===Table 55. Synopsis of Terminology: Restrictive and Alternative Subtypes=== |