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Directory:Jon Awbrey/Papers/Differential Logic (view source)
Revision as of 03:08, 10 June 2009
, 03:08, 10 June 2009→Note 18: markup
In the case of <math>V_4 = (G, \cdot),</math> where <math>G\!</math> is the ''underlying set'' <math>\{ \operatorname{e}, \operatorname{f}, \operatorname{g}, \operatorname{h} \},</math> we have the 3-adic relation <math>L(V_4) \subseteq G \times G \times G</math> whose triples are listed below:
In the case of <math>V_4 = (G, \cdot),</math> where <math>G\!</math> is the ''underlying set'' <math>\{ \operatorname{e}, \operatorname{f}, \operatorname{g}, \operatorname{h} \},</math> we have the 3-adic relation <math>L(V_4) \subseteq G \times G \times G</math> whose triples are listed below:
{| align="center" cellpadding="6" width="90%"
| align="center" |
<math>\begin{matrix}
(\mathrm{e}, \mathrm{e}, \mathrm{e}) &
(\mathrm{e}, \mathrm{f}, \mathrm{f}) &
(\mathrm{e}, \mathrm{g}, \mathrm{g}) &
(\mathrm{e}, \mathrm{h}, \mathrm{h})
\\[6pt]
(\mathrm{f}, \mathrm{e}, \mathrm{f}) &
(\mathrm{f}, \mathrm{f}, \mathrm{e}) &
(\mathrm{f}, \mathrm{g}, \mathrm{h}) &
(\mathrm{f}, \mathrm{h}, \mathrm{g})
\\[6pt]
(\mathrm{g}, \mathrm{e}, \mathrm{g}) &
(\mathrm{g}, \mathrm{f}, \mathrm{h}) &
(\mathrm{g}, \mathrm{g}, \mathrm{e}) &
(\mathrm{g}, \mathrm{h}, \mathrm{f})
\\[6pt]
(\mathrm{h}, \mathrm{e}, \mathrm{h}) &
(\mathrm{h}, \mathrm{f}, \mathrm{g}) &
(\mathrm{h}, \mathrm{g}, \mathrm{f}) &
(\mathrm{h}, \mathrm{h}, \mathrm{e})
\end{matrix}</math>
|}
<pre>
<pre>
It is part of the definition of a group that the 3-adic
It is part of the definition of a group that the 3-adic
relation L c G^3 is actually a function L : G x G -> G.
relation L c G^3 is actually a function L : G x G -> G.