[Om3] binary vs n-ary relations

[Bruce Miller]

Professor James Davenport wrote:
> On Wed, 24 Sep 2008, Paul Libbrecht wrote:
>> Making them n-ary doesn't solve the classical writing of
>>  a < b > c
>> which is used quite often still.
> Is it? Oh my God ....

I agree; that's scary!
OTOH, it is quite common to string different,
but "consistent", relations together:
   a = b > c = d >= e >> f

Sometimes the consistency is dubious:
   a = b
     approx c
     approx d
(where the approx is indicating that the rhs has
been somehow approximated, expanded or whatever).
I've seen cases where it seemed that the d
was more likely an approximation of a than c!

And then there's the occasional
    a > b,c > d
which _sometimes_ means:
   (a > b) & (a > c) & (b > d) & (c > d)
rather than  just
   (a > b) & (c > d)

> I assume one can therefore say a < b > c < d > e ...
> (where e is not necessarily the base of the natural logarithms)
>> So another workaround is neither whatsoever and I think it should be at the
>> notations' level.
> Hear here.

Indeed; while I do think it is appealing to be able to
preserve this notational structure, nary relations
only scratch the surface.  Short of a contrived
multi-relation construct, this situation would
seem to be best solved (at a MML level) by
a <semantics> pairing of the desired notation
and the underlying logic, probably using sharing/id/ref.

> James
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-- 
bruce.miller at nist.gov
http://math.nist.gov/~BMiller/