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, 02:31, 5 July 2007→Transformations of Type '''B'''<sup>2</sup> → '''B'''<sup>2</sup>: wiki table
Table 64 shows how the action of the transformation ''F'' on cells or points is computed in terms of coordinates.
Table 64 shows how the action of the transformation ''F'' on cells or points is computed in terms of coordinates.
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Table 64. Transformation of Positions
|+ '''Table 64. Transformation of Positions'''
|- style="background:paleturquoise"
| u v | x | y | x y | x(y) | (x)y | (x)(y) | X% = [x, y] |
| ''u'' ''v''
| ''x''
| | | | | | | | ^ |
| ''y''
| 0 0 | 0 | 1 | 0 | 0 | 1 | 0 | | |
| ''x'' ''y''
| | | | | | | | |
| ''x'' (''y'')
| 0 1 | 1 | 0 | 0 | 1 | 0 | 0 | F |
| (''x'') ''y''
| | | | | | | | = |
| (''x'')(''y'')
| 1 0 | 1 | 0 | 0 | 1 | 0 | 0 | <f , g> |
| ''X''<sup> •</sup> = [''x'', ''y'' ]
| | | | | | | | |
|-
| 1 1 | 1 | 1 | 1 | 0 | 0 | 0 | ^ |
| width="12%" |
| | | | | | | | | |
{| align="center" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%"
| 0 0
| | ((u)(v)) | ((u, v)) | u v | (u,v) | (u)(v) | 0 | U% = [u, v] |
|-
| 0 1
</pre>
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{| align="center" border="0" cellpadding="2" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:100%"
| ↑
|-
| ''F''
|-
| ‹''f'', ''g'' ›
|-
| ↑
|}
|-
|
| ((''u'')(''v''))
| ((''u'', ''v''))
| ''u'' ''v''
| (''u'', ''v'')
| (''u'')(''v'')
| ( )
| ''U''<sup> •</sup> = [''u'', ''v'' ]
|}
<br>
Table 65 extends this scheme from single cells to arbitrary regions of the source and target universes, and illustrates a form of computation that can be used to determine how a logical transformation acts on all of the propositions in the universe. The way that a transformation of positions affects the propositions, or any other structure that can be built on top of the positions, is normally called the ''induced action'' of the given transformation on the system of structures in question.
Table 65 extends this scheme from single cells to arbitrary regions of the source and target universes, and illustrates a form of computation that can be used to determine how a logical transformation acts on all of the propositions in the universe. The way that a transformation of positions affects the propositions, or any other structure that can be built on top of the positions, is normally called the ''induced action'' of the given transformation on the system of structures in question.
