12,080
edits
Changes
Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 18:24, 30 April 2009
, 18:24, 30 April 2009→Commentary Note 11.7
\\[6pt]
\\[6pt]
& = &
& = &
\{ (x, y) \in L : x = u \}
\{ (u, y) \in L \}
\\[6pt]
\\[6pt]
& = &
& = &
\\[6pt]
\\[6pt]
& = &
& = &
\{ (x, y) \in L : y = v \}
\{ (x, v) \in L \}
\\[6pt]
\\[6pt]
& = &
& = &
\text{the set of all ordered pairs in}~ L ~\text{incident with}~ v \in Y.
\text{the set of all ordered pairs in}~ L ~\text{incident with}~ v \in Y.
\end{array}</math>
|}
The following definitions are also useful:
{| align="center" cellspacing="6" width="90%"
|
<math>\begin{array}{lll}
u \cdot L
& = &
\operatorname{proj}_2 (u \star L)
\\[6pt]
& = &
\{ y \in Y : (u, y) \in L \}
\\[6pt]
& = &
\text{the elements of}~ Y ~\text{that are}~ L\text{-related to}~ u.
\\[9pt]
L \cdot v
& = &
\operatorname{proj}_1 (L \star v)
\\[6pt]
& = &
\{ x \in X : (x, v) \in L \}
\\[6pt]
& = &
\text{the elements of}~ X ~\text{that are}~ L\text{-related to}~ v.
\end{array}</math>
\end{array}</math>
|}
|}