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<div class="moz-cite-prefix">Mathematical characters in Unicode 1.1
come from a variety of sources. However, unlike the later process
of adding characters there usually is not a detailed paper trail.
Instead of tracking down exemplary uses for each character, the
early drafts of Unicode often relied on existing character and
symbol sets, for example SGML entity sets.</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">The main reason for that approach was
the goal of being able to express in Unicode any character or
symbol that could already be used digitally. Where available (and
not contra indicated for some reason), the names were based on
names in existing sets.</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">To locate the true origin of such early
symbols, you would have to look for usage that was common enough
no later than the early or mid eighties to have been reflected in
some of the precursor sets.</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">Documents from this millennium at best
reflect use (or re-use) of an existing symbol.</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">A./</div>
<div class="moz-cite-prefix"><br>
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<div class="moz-cite-prefix">PS: as Markus has said, we don't change
the formal names, but if the existing name poorly reflects actual
(or modern) use of a character, such use can be indicated with
annotations. However, that would apply only to very common uses,
or cases where the formal name suggests a use that "never was".<br>
</div>
<div class="moz-cite-prefix"><br>
</div>
<div class="moz-cite-prefix">On 9/3/2021 10:34 AM, Marius Spix via
Unicode wrote:<br>
</div>
<blockquote type="cite" cite="mid:20210903193443.546efe31@spixxi">
<pre class="moz-quote-pre" wrap="">It seems that the symbol U+22B6 has been used first by Joachim Kock
from UAB Barcelona Maths Department. He is also using on a website, last
modified in 2006, four years before the already mentioned paper
“Polynomial functors and opetopes” had been published.[1]
The symbol has been “borrowed” from other authors, e. g. [2], [3]
Maybe Mr. Kock can provide more information about the origin of that
character and also answer the other questions.
[1] <a class="moz-txt-link-freetext" href="https://mat.uab.cat/~kock/cat/zoom/examples.html">https://mat.uab.cat/~kock/cat/zoom/examples.html</a>
[2]
<a class="moz-txt-link-freetext" href="http://www.lix.polytechnique.fr/Labo/Samuel.Mimram/docs/mimram_optt.pdf">http://www.lix.polytechnique.fr/Labo/Samuel.Mimram/docs/mimram_optt.pdf</a>
[3] <a class="moz-txt-link-freetext" href="https://github.com/ggreif/seminar-opetope">https://github.com/ggreif/seminar-opetope</a> (with diamonds instead of
circles, though)
On Fr, 3 Sep 2021 18:07:14 +0200
Ivan Panchenko via Unicode <a class="moz-txt-link-rfc2396E" href="mailto:unicode@corp.unicode.org"><unicode@corp.unicode.org></a> wrote:
</pre>
<blockquote type="cite">
<pre class="moz-quote-pre" wrap="">Consider the following character names:
ORIGINAL OF (⊶, U+22B6)
IMAGE OF (⊷, U+22B7)
I find “original” as a noun strange in this context. How about
“origin”, “domain” or “source”? However, the only mathematical use of
“⊶” that I found was in the context of zooms as defined in section
1.5 here: <a class="moz-txt-link-freetext" href="https://arxiv.org/pdf/0706.1033.pdf">https://arxiv.org/pdf/0706.1033.pdf</a>
This work is from 2010, but the character already existed in Unicode
1.0.0, so I am not sure what it was supposed to mean after all. Any
hint? Perhaps U+2290 ⊐ SQUARE ORIGINAL OF was supposed to have the
same meaning as U+22B6 (why else would it be named this way?).
Furthermore:
SUBSET OF WITH NOT EQUAL TO (⊊, U+228A)
LESS-THAN BUT NOT EQUAL TO (≨, U+2268)
SQUARE ORIGINAL OF OR NOT EQUAL TO (⋥, U+22E5)
The first of these names employs the word “with” to describe how
U+228A looks like, the second one employs the word “but” to describe
what U+2268 means. (A bit inconsistent, but fine so far.)
In the third one, I find the “or not equal to” part strange. Would
“BUT not equal to” not be more plausible?
Sidenote (not an issue with Unicode): I find it remarkable that while
“≤” is used to mean ‘is less than OR equal to’, we use “⊊” for ‘is a
subset of AND not equal to’, which breaks the analogy. I might prefer
“⊊︀” (with stroke through bottom members) to “⊊” for this reason. The
file bsymbols.mf of amsfonts deviously contains “cmchar "Subset or
not equal to sign"”. Cf. Paul Taylor for a criticism of the use of
“⊂” for the proper subset relation:
<a class="moz-txt-link-freetext" href="https://books.google.com/books?id=iSCqyNgzamcC&pg=PA75&q=%22but+strict+inclusion+is+neither+primitive%22">https://books.google.com/books?id=iSCqyNgzamcC&pg=PA75&q=%22but+strict+inclusion+is+neither+primitive%22</a>
Schröder (1890) actually used a symbol (in the strict sense) that
looked similar to our “⊂” but went up- and downwards like the
less-than sign; I do not advocate reintroducing it either since we
also write “∩” and “∪” (analogously to “∧” and “∨”) with parallel
lines.
</pre>
</blockquote>
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</blockquote>
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