best practicesspacing
When I work with quantifiers I noted that are very close to the other symbols and the result does not look good, for example
$\exists a\in\mathbb{R}\exists b\in\mathbb{R}\forall c\in\mathbb{R}\forall d\in\mathbb{R}$
Which is the proper form to write quantifiers?
Posting this as an answer because it is too long for a comment, but I do not aim at exhaustivity (or objectivity, as a matter of fact).
My first suggestion would be, whatever you do regarding the choice of terms to index, to use and abuse the | syntax in your indexing commands (either manually, or by creating your own command that does it):
It works for page ranges, by successively indexing:
\index{something|(} ... \index{something|)}
It also works for whatever formatting commands you may want to add to the page number. Essentially, you can put any control sequence name after |, provided that its last argument (if any) is the implicit page number.
For instance, when something is located in a footnote, I defined:
\newcommand{\note}[1]{#1~(\emph{n.})}
and I can then use: \index{something|note} – no backslash – which outputs:
something, 36 (n.)
This could be used to put the page number in boldface, or something of that kind. Identifying the principal reference(s) sounds like a good idea to me, though it is a matter of personal taste (some people do it, some don't).
Now, regarding your question proper, the general idea is that you should index terms where it makes the most sense and/or where the reader is most likely to look for them.
To me, this would mean that if you have an expression with a noun and an adjective, like "British imperialism", you would index:
imperialism, British, 39
and eventually (adjectives shouldn't normally be index headings):
British imperialism, see imperialism
Regarding abbreviations, the same logic could apply. Since the abbreviation stands for the full expression, it would seem logical redirect the reader there, a bit like in a glossary. So, unlike what you proposed in your question, I would be kind to the reader (if he is not strictly speaking from your field, chances are he does not remember all abbreviations), and suggest:
EIC, see East India Company (British)
East India Company (British), 45
But there could be many variants; for instance, an equally valid construct could be:
East India Company (EIC), 45
Then, there are the complex cases where you have two nouns (or words) of approximatively equal semantic weight, and it is not clear which one should be indexed. Here, it depends on the context, I suppose.
If you think that the reader could reasonably look up either term, then index both with a "see" construct.
If both terms are already indexed in their own right, for other reasons (with sub-entries perhaps), then it is almost always worthwhile to redirect the reader with a "see" construct.
Returning to my first example, while I would not necessarily (just eventually) index "British imperialism" on its own just for a "see" construct, if I already had two significant entries for "britain" and "imperialism", I would definitely write:
Britain, 2, 18-29, 23: economy, 5, 33–39; imperialism (see imperialism)
imperialism: British, 37; Dutch, 74; French, 82
I find it good practice, as far as possible, to create matching index headings; what I really mean is, consistency. If you have two things that have a similar logical structure, index them in the same way. Say, if you are indexing people's names to refer the reader to biographical information, try to construct the sub-entries in the same fashion for everyone. I am not saying they should be strictly identical, but that when similarities (in sub-entries) do occur, you should make sure they appear as such in your index.
Say, don't index:
Smith, John: Years in London, 46
and a couple of entries later:
Turner, Jack: Lived in Manchester, 32
That's inconsistent and awkward.
Here is the Chicago Manual of Style's stand on "see" references:
See references direct a reader from, for example, an informal term to a technical one, a pseudonym to a real name, an inverted term to a noninverted one. They are also used for variant spellings, synonyms, aliases, abbreviations, and so on.
The Oxford Guide to Style is substantially similar on that matter. Neither give very precise information regarding abbreviations and other complex issues, but they have great chapters on indexing proper names and punctuating index entries.
Finally, regarding indexing processes, while I agree with most of the comments so far – that most of the work takes place when you are almost done with the writing – I think there are some things you can index on the go, as "flags". If a word is so important that it makes a section heading, or that you define it in a precise way, it will be indexed under that heading anyway, so you may as well do it while writing.
This will give you bare bones for your index, which you can then improve when everything else is done. I find it helpful to print the index (with MakeIndex or on paper), then I can decide which entries are superfluous, which are lacking, which could be merged or rearranged and modify my document accordingly.
If you replace some of the symbolism with words from natural language, I think you get a much clearer and cleaner result; the most natural choice for the list is an enumerate environment; here's one possibility:
\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
We must have $(a^i,b^i,c^i) \in X^i(d)$, where $X^i(d)$ is the set of all triples $(a,b,c) \in \mathbb R^A \times \mathbb R^B \times \mathbb R^C $ such that
\begin{enumerate}
\item $d_0 \cdot (a_0 - b_0) + d_1 \cdot (b_0 - c_0) \leq 0$,
\item $\smash[b]{\sum_j c_j b^j} \leq d_j$, and
\item $\forall k \geq 1, d_k \cdot \left(a_k - b^h_k - F_k(x_{k^*})\right) \leq
\sum_k (b_k-c_k) \cdot \min\bigl(d_k \cdot G^j_k, m_k \bigr)$.
\end{enumerate}
\end{document}
Best Answer
It depends on the context.
If this is part of a piece of text, then you might consider Peter Grill's suggestion:
On the other hand, if the quantifiers are part of a logical formula, you might consider a dot between the quantifiers, like this:
This dot notation is inherited, I think, from Russell and Whitehead's Principia Mathematica, and is quite widely used, particularly in computer science. A comma between quantifiers is quite unusual, though it does appear in the syntax of the Coq theorem prover.
The comma notation becomes awkward when you want to quantify several variables at the same time, because then you have two different types of comma in the same formula:
In such cases, you might consider putting just a space between the variables, like this:
The idea of putting spaces between variables, rather than commas, is taken from the syntax of the Isabelle theorem prover.