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Revision as of 16:24, 14 June 2009

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