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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 01:06, 13 April 2009
, 01:06, 13 April 2009→Commentary Note 11.7
In the light of these considerations, the local flags of a 2-adic relation <math>L \subseteq X \times Y</math> may be formulated as follows:
In the light of these considerations, the local flags of a 2-adic relation <math>L \subseteq X \times Y</math> may be formulated as follows:
{| cellpadding="4"
{| align="center" cellspacing="6" width="90%"
| ''L''<sub>''u''.''X''</sub>
|
<math>\begin{array}{lll}
L_{u \star X}
& = &
\{ (x, y) \in L : x = u \}
\\[6pt]
& = &
\text{the set of all ordered pairs in}~ L ~\text{incident with}~ u \in X.
\\[9pt]
L_{v \star Y}
& = &
\{ (x, y) \in L : y = v \}
\\[6pt]
& = &
\text{the set of all ordered pairs in}~ L ~\text{incident with}~ v \in Y.
\end{array}</math>
|}
|}
|}
|}
The local flag ''E''<sub>3.''X''</sub> is displayed here:
The local flag <math>E_{3 \star X}</math> is displayed here:
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"
|}
|}
The local flag ''E''<sub>2.''Y''</sub> is displayed here:
The local flag <math>E_{2 \star Y}</math> is displayed here:
{| align="center" cellspacing="6" width="90%"
{| align="center" cellspacing="6" width="90%"