MyWikiBiz, Author Your Legacy — Wednesday April 02, 2025
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, 14:08, 3 May 2009
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| height="40" | <math>S \subseteq X \times X\!</math> is the 2-adic relation associated with the relative term <math>\mathit{s} = \text{servant of}\,\underline{~~~~}.</math>
| height="40" | <math>S \subseteq X \times X\!</math> is the 2-adic relation associated with the relative term <math>\mathit{s} = \text{servant of}\,\underline{~~~~}.</math>
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{| align="center" cellspacing="6" width="90%"
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<pre>
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a b c d e f g h i
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o o o o o o o o o X
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/ \ : | : |
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/ \ 0 1 0 1 L
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/ \ : | : |
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o o o o + - + + o X
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\ | / : : | |
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\ | / 0 0 1 1 S
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\|/ : : | |
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o o o o o o o o o X
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a b c d e f g h i
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</pre>
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|}
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There is a "servant of every lover of" link between <math>u\!</math> and <math>v\!</math> if and only if <math>u \cdot S ~\supseteq~ L \cdot v.</math> But the vacuous inclusions will make this non-intuitive.
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{| align="center" cellspacing="6" width="90%"
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| <math>(\mathfrak{S}^\mathfrak{L})_{uv} ~=~ \prod_{x \in X} \mathfrak{S}_{ux}^{\mathfrak{L}_{xv}}</math>
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In other words, <math>(\mathfrak{S}^\mathfrak{L})_{uv} = 0</math> if and only if there exists an <math>x \in X</math> such that <math>\mathfrak{S}_{ux} = 0</math> and <math>\mathfrak{L}_{xv} = 1.</math>
==References==
==References==