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Revision as of 16:24, 14 June 2009
, 16:24, 14 June 2009→Note 14: markup
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Line 3,042:
It has long been customary to omit the implicit plus signs
−in these matrical displays, but I have restored them here
−simply as a way of separating terms in this blancophage
−web format.
−For at least a little while, I will make explicit+the distinction between a "relative term" like m+and a "relation" like M c X x X, but it is best+to think of both of these entities as involving+different applications of the same information,+and so we could just as easily write this form:+ m =+ m_aa a:a + m_ab a:b + m_ac a:c ++ m_ba b:a + m_bb b:b + m_bc b:c ++ m_ca c:a + m_cb c:b + m_cc c:c+By way of making up a concrete example,+let us say that M is given as follows:
−
− a is a marker for a
−
− a is a marker for b
−
− b is a marker for b
−
− b is a marker for c
−
− c is a marker for c
−
− c is a marker for a
−
−In sum, we have this matrix:
−
− M =
−
− 1 a:a + 1 a:b + 0 a:c +
−
− 0 b:a + 1 b:b + 1 b:c +
−
− 1 c:a + 0 c:b + 1 c:c
−
−</pre>
|}
|}
−<pre>
+For at least a little while, I will keep explicit the distinction between a ''relative term'' like <math>\mathit{m}\!</math> and a ''relation'' like <math>M \subseteq X \times X,</math> but it is best to think of both of these entities as involving different applications of the same information, and so we could just as easily write this form:
−{| align="center" cellpadding="6" width="90%"
−| align="center" |
−<math>
−m \quad = \quad
−\begin{bmatrix}
−m_{aa}(a\!:\!a) & m_{ab}(a\!:\!b) & m_{ac}(a\!:\!c)
+\\
+m_{ba}(b\!:\!a) & m_{bb}(b\!:\!b) & m_{bc}(b\!:\!c)
+\\
+m_{ca}(c\!:\!a) & m_{cb}(c\!:\!b) & m_{cc}(c\!:\!c)
+\end{bmatrix}
+</math>
+|}
−By way of making up a concrete example, let us say that <math>M\!</math> is given as follows:
−{| align="center" cellpadding="6" width="90%"
+| align="center" |
+<math>\begin{array}{l}
+a ~\text{is a marker for}~ a
+\\
+a ~\text{is a marker for}~ b
+\\
+b ~\text{is a marker for}~ b
+\\
+b ~\text{is a marker for}~ c
+\\
+c ~\text{is a marker for}~ c
+\\
+c ~\text{is a marker for}~ a
+\end{array}</math>
+|}
−In sum, the relative term <math>\mathit{m}\!</math> and the relation <math>M\!</math> are both represented by the following matrix:
−{| align="center" cellpadding="6" width="90%"
+| align="center" |
+<math>\begin{bmatrix}
+1 \cdot (a\!:\!a) & 1 \cdot (a\!:\!b) & 0 \cdot (a\!:\!c)
+\\
+0 \cdot (b\!:\!a) & 1 \cdot (b\!:\!b) & 1 \cdot (b\!:\!c)
+\\
+1 \cdot (c\!:\!a) & 0 \cdot (c\!:\!b) & 1 \cdot (c\!:\!c)
+\end{bmatrix}</math>
+|}
−I think this much will serve to fix notation and set up the remainder of the account.
−I think that will serve to fix notation
−and set up the remainder of the account.
−==Note 15==
==Note 15==
