Re: an odd ambiguity

One more interpretation is the use of the pipe-character as separator 
for coordinates in German’s schoolbooks.

E.g.: http://oriesen.ch/doku/Raumgeometrie1S.pdf gives an example of 
that (on the second page): copied from the PDF: _Zeichne in der linken 
Figur die Punkte P ( 6 |3 |3 ) , Q ( 0 |4 |6 ) und R ( 1 |5 |3 ) ein._ 
(Which has quite a different spacing than in the PDF). In this usage and 
in this work, it seems that the spacing should be the same on both 
sides.

As an “intent”, the whole notation made of “(“, the “|” and 
“)” should be considered. Is this planned in our intents syntax? 
Should the intent be on the mrow and can we avoid to pronounce the 
pipes?

paul


On 4 Aug 2021, at 6:27, Neil Soiffer wrote:

> We've mentioned how ambiguous "|" can be, but I don't remember seeing
> anyone mentioning this example:
> { x   ∣ x  ∣ 10}
> The set of all x such that x divides 10.
>
> In one expression are both the low priority separator "such that" and 
> the
> medium priority relational operator "divides" (both are infix). There 
> are
> two characters that *could *be used: vertical bar (U+007C) and divides
> (U+2223).  The Unicode Standard indicates that both should be U+2223 
> (I'm
> not sure that equivalence is correct)
>
> In TeX, there seems to be agreement that the first bar is be \mid.
> However, there
> seems to be disagreement for what to use for the second bar.
> <https://tex.stackexchange.com/questions/498/mid-vertical-bar-vert-lvert-rvert-divides>
> Some people suggest \mid, others "|", and still others \divides (which 
> only
> exists in the MnSymbol package AFAIK). There are spacing differences 
> and
> maybe height differences. Using different macros means there is a 
> potential
> semantic distinction if the author actually uses them as opposed to 
> using
> the ASCII "|". A reason TeX distinguishes them is that the spacing 
> around
> the vertical bar differs a little. Someone will surely correct me on 
> this
> if I'm wrong, but the spacing of these two uses is opposite their
> contextual meaning. TeX considers \mid to be a relational operator, 
> but
> relational operators return boolean values -- \mid is really a
> separator/punctuation. On the other hand, \divides really is a 
> relation (m
> divides n is either true or false), but it is spaced as a binary 
> operator
> (at least in this context). Typographically, this is what is supposed 
> to
> happen, but it seems counter-intuitive. Very strange.
>
> What does this mean for MathML? One thing is that in practice, 
> software
> can't be sure the correct symbol is used in MathML (I leave it to 
> someone
> else to report what TeX, ASCIIMath, and WYSIWYG editors use). The 
> other
> issue is what the operator dictionary should say about the spacing and
> priority for these two symbols. Currently they both have the same 
> spacing
> and priority, but that seems wrong.
>
> Thoughts?
>
>     Neil