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Presently, the distinction between indirect pointers and direct pointers, that is, between virtual copies and actual views of an objective domain, is not yet relevant here, being a dimension of variation that the discussion is currently abstracting over.

Presently, the distinction between indirect pointers and direct pointers, that is, between virtual copies and actual views of an objective domain, is not yet relevant here, being a dimension of variation that the discussion is currently abstracting over.

I would like to record here, in what is topically the appropriate place, notice of a number of open questions that will have to be addressed if anyone desires to make a consistent calculus out of this caret notation.  Perhaps it is only because the franker forms of liaison involved in the caret couple a^b are more subject to the vagaries of syntactic elision than the corresponding bindings of the anglish ligature <a, b>, but for some reason or other the circumflex character of these diacritical notices are much more liable to suggest various forms of elaboration, including higher order generalizations and information theoretic partializations of the very idea of n tuples and sequences.

<p align="center">'''Fragments'''</p>

One way to deal with the problems of partial information ...

I would like to record here, in what is topically the appropriate place, notice of a number of open questions that will have to be addressed if anyone desires to make a consistent calculus out of this binder notation.  Perhaps it is only because the franker forms of liaison involved in the couple <math>a \widehat{~} b\!</math> are more subject to the vagaries of syntactic elision than the corresponding bindings of the anglish ligature <math>(a, b),\!</math> but for some reason or other the circumflex character of these diacritical notices are much more liable to suggest various forms of elaboration, including higher order generalizations and information-theoretic partializations of the very idea of <math>n\!</math>-tuples and sequences.

1. Carets linkages can be chained together to form sequences of indications or n tuples, without worrying too much about the order of collecting terms in the corresponding angle brackets.

1. Carets linkages can be chained together to form sequences of indications or n tuples, without worrying too much about the order of collecting terms in the corresponding angle brackets.

  ^x  =      < , x> x^  =  <x, >    ?

  ^x  =      < , x> x^  =  <x, >    ?

^^x  =  < , < , x>> x^^  =  <<x, >, >  ?

^^x  =  < , < , x>> x^^  =  <<x, >, >  ?

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 ...