Motion P1788/M0034.01 Notation:NO
My vote on M0034.01 Notation is NO.
Double-struck letters fit with standard mathematical notation for
number sets, and I have no disagreement with that. If I want a
double-struck R, it's available, with a bit of work and research, as
Unicode U+211D, and I can even cut and paste that into any Unicode-aware
"plaintext" e-mail. Look! ℝ! A real number!
We must ensure, however, that we adopt a standard that *can* work
with a global, worldwide standard for text which is Unicode, and, for
correctness and our sanity, it should be likely to survive
cut-and-paste, and needs to be communicable in emails, programming
languages, and other modern constructs that support Unicode. Even if
you can manage, with more research, to compose a Unicode ℝ character
with overline, such as by the sequence U+211D U+0305, to make ℝ̅, it is
questionable if it will survive cutting-and-pasting, or even if its
display will be visible and distinguishable. (For example, I can't tell
in Thunderbird if it's an overline or an underline of an above
character. My cut-and-paste tests indicate that while many
Unicode-aware applications can handle the single ℝ character, they do
bad things with the composed character with overline, like displaying
the overbar as a separate character to the right, or silently losing it
entirely.)
I would prefer the conventions used in the literature (e.g. Hansen,
Walster) of using ℝ* to indicate the extended reals, for example. It's
easier to typeset, cut, paste, see, read, pronounce out loud,
disambiguate, etc.
Overlines are also too overloaded with meanings: negation of a term
in set theory, vectors, complex conjugates, etc.
Any proposal for notation must include explicit analysis of how those
symbols are to be typeset in the modern world (e.g. Unicode.) If we can
write what we mean on an e-mail list like this, rather than writing
impenetrable LaTeX that stops a reader cold, then our notation is closer
to being usable, and closer to being adopted by the world at large.
--
Alan Eliasen
eliasen@xxxxxxxxxxxxxx
http://futureboy.us/