- From: Neil Soiffer <soiffer@alum.mit.edu>
- Date: Wed, 4 Aug 2021 20:52:15 -0700
- To: David Farmer <farmer@aimath.org>
- Cc: "www-math@w3.org" <www-math@w3.org>
- Message-ID: <CAESRWkB6=cuotawwy-gqG5bEf6nG8+Ov2R37b_EuMaN9HEBfvw@mail.gmail.com>

> d(n) = |{ d | d||n| }| You definitely trump my example, even without the absolute value. Neil On Wed, Aug 4, 2021 at 4:07 AM David Farmer <farmer@aimath.org> wrote: > > The number theoretic function d(n) equals the number of > positive divisors of the absolute value of n . In symbols: > > d(n) = |{ d | d||n| }| > > Moving left-right and outside-in: > > d is the name of the function on the left > (that is a common name for that function, \tau is the other common name) > > |A| cardinality of the set A > > d is a bound variable on the right side > (it actually is common to do that in this context > > | "such that" separator > > d| "divides" relation > > |n| absolute value of n > (That is the only silly part of this example, because the > divisors of n are the same as the divisors of -n , > so the absolute value is not actually needed.) > > > > On Wed, 4 Aug 2021, Paul Libbrecht wrote: > > > > > 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. 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 > > > > > >

Received on Thursday, 5 August 2021 03:52:28 UTC