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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
Revision as of 21:12, 20 November 2012
, 21:12, 20 November 2012→6.33. Sign Relational Complexes: markup
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Linkages can be chained together to form sequences of indications or <math>n\!</math>-tuples, without worrying too much about the order of collecting terms in the corresponding angle brackets.
a^b^c = <a, b, c> = <a, <b, c>> = <<a, b>, c>.
{| align="center" cellspacing="8" width="90%"
|
<math>\begin{matrix}
a \widehat{~} b \widehat{~} c
& = &
(a, b, c)
& = &
(a, (b, c))
& = &
((a, b), c).
\end{matrix}</math>
|}
These equivalences depend on the existence of natural isomorphisms between different ways of constructing n place product spaces, that is, on the associativity of pairwise products, a not altogether trivial result (MacLane, CatWorkMath, ch. 7).
These equivalences depend on the existence of natural isomorphisms between different ways of constructing <math>n\!</math>-place product spaces, that is, on the associativity of pairwise products, a not altogether trivial result (Mac Lane, CatWorkMath, ch. 7).
Higher Order Indications (HOIs)?
{| align="center" cellspacing="8" width="90%"
|
<math>\begin{matrix}
\widehat{~} x & = & (~, x) & ?
\\[4pt]
x \widehat{~} & = & (x, ~) & ?
\\[4pt]
\widehat{~}~\widehat{~} x & = & (~, (~, x)) & ?
\\[4pt]
x \widehat{~}~\widehat{~} & = & ((x, ~), ~) & ?
\end{matrix}</math>
|}
<pre>
In talking about properties and classes of relations, one would like to refer to "all relations" as forming a topic of potential discussion, and then take it as a background for contemplating ...
In talking about properties and classes of relations, one would like to refer to "all relations" as forming a topic of potential discussion, and then take it as a background for contemplating ...