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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 20:00, 27 April 2009
, 20:00, 27 April 2009→Commentary Note 12.1
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<math>\begin{array}{lll}
<math>\begin{array}{lll}
L_{u \,\text{at}\, 1} & = & \{ (u, x) \in L \}
u \cdot L
& = &
L_{u \,\text{at}\, 1}
\\[6pt]
\\[6pt]
& = & \text{the set of ordered pairs in}~ L ~\text{that have}~ u ~\text{in the 1st place}.
& = & \{ (u, x) \in L \}
\\[6pt]
& = &
\text{the set of ordered pairs in}~ L ~\text{that have}~ u ~\text{in the 1st place}.
\\[9pt]
\\[9pt]
L_{v \,\text{at}\, 2} & = & \{ (x, v) \in L \}
L \cdot v
& = &
L_{v \,\text{at}\, 2}
\\[6pt]
& = &
\{ (x, v) \in L \}
\\[6pt]
\\[6pt]
& = & \text{the set of ordered pairs in}~ L ~\text{that have}~ v ~\text{in the 2nd place}.
& = &
\text{the set of ordered pairs in}~ L ~\text{that have}~ v ~\text{in the 2nd place}.
\end{array}</math>
\end{array}</math>
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{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
| <math>\mathit{l}^\mathrm{w} ~=~ \bigcap_{x \in W} L_{x \,\text{at}\, 2}</math>
| <math>\mathit{l}^\mathrm{w} ~=~ \bigcap_{x \in W} L \cdot x</math>
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