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MyWikiBiz, Author Your Legacy — Saturday October 05, 2024
Jump to navigationJump to search→Table 54. Cast of Characters: Expansive Subtypes of Objects and Operators
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{| 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" | <p>W</p>
| valign="top" | <p>W :</p>
<p>''U''<sup> •</sup> → E''U''<sup> •</sup> ,</p>
<p>''X''<sup> •</sup> → E''X''<sup> •</sup> ,</p>
<p>(''U''<sup> •</sup>→''X''<sup> •</sup>) →<br>
E''U''<sup> •</sup>→E''X''<sup> •</sup>) ,</p>
<p>For each W in the set:<br>
{<math>\epsilon</math>, <math>\eta</math>, E, D, d}</p>
| valign="top" | <p>Operator</p>
| valign="top" | <p> <p>
<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>
<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>
<p> <br> </p>
|-
|
|
|
|
|-
| <font face="lucida calligraphy">A<font>
| {''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>}
| Alphabet
| [''n''] = '''n'''
|-
| ''A''<sub>''i''</sub>
| {(''a''<sub>''i''</sub>), ''a''<sub>''i''</sub>}
| Dimension ''i''
| '''B'''
|-
| ''A''
|
〈<font face="lucida calligraphy">A</font>〉<br>
〈''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>〉<br>
{‹''a''<sub>1</sub>, …, ''a''<sub>''n''</sub>›}<br>
''A''<sub>1</sub> × … × ''A''<sub>''n''</sub><br>
∏<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''*
| (hom : ''A'' → '''B''')
| Linear functions
| ('''B'''<sup>''n''</sup>)* = '''B'''<sup>''n''</sup>
|-
| ''A''^
| (''A'' → '''B''')
| Boolean functions
| '''B'''<sup>''n''</sup> → '''B'''
|-
| ''A''<sup>•</sup>
|
[<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>
===Table 55. Synopsis of Terminology: Restrictive and Alternative Subtypes===
===Table 55. Synopsis of Terminology: Restrictive and Alternative Subtypes===
