alignitemizeline-breaking
The following code
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{itemize}
\item
\begin{align}
a&=b\\
&=d
\end{align}
\item
\begin{equation}
a=b\\
=d
\end{equation}
\end{itemize}
\end{document}
produces
How to avoid the linebreak after the bullet and have the equations (1 and 3) begin on the same line (with the bullet)? I should perhaps emphasize that I want to preserve the numbering of the equations.
I would definitely go the second way with $\displaystyle: I find that it looks strange to have something centered after a bullet. To get the vertical alignment correct, just add [t] after \begin{aligned}, where "t" means "top". (See also the top of page 8 of the User's guide for the amsmath Package.)
you've already separated the different elements, providing spaces between the distinct equations comprising each language and separately coding these equations as math (even though the space between the first two is, probably inadvertently, omitted). unfortunately, these spaces don't fall in a place that is optimal for tex to break the line.
the ultimate goal is for what is presented to be understood.
there are two parts to this recommendation.
first, the words "milk, curry, rice" are, as you say, constants, and as such should be
in a text font, preferably not italic in this context, even though they're part of the
math expression. as coded in your original, they are typeset as strings of variables
multiplied together. these could be coded as \mathrm{<word>}, but that doesn't help
with line breaking. it also wouldn't leave spaces after the commas, although in this
situation, whether spaces are visible there or not wouldn't be misunderstood by a reader.
another way to approach these is to recognize them as text, and input them as, for example,
$\mathcal{C}_o=\{\text{milk, curry, rice}\}$
but this doesn't help with line breaking either, since in this context, the only "allowable" break is after the equals sign.
so, second part of suggestion, take advantage of the fact that a reader isn't likely to misunderstand what is meant if a line is broken within that string of constants, and (temporarily) terminate the math after the opening brace, and reinstate it for the ending brace:
$\mathcal{C}_o=\{$milk, curry, rice$\}$
to illustrate, using a forced line break for the "all math" instance, compare these two lines:
here's the input that produced the image:
\begin{itemize}
\item The language of enquiry $\mathcal{L}$ is given by
$\mathcal{C}_o=\{milk, curry, rice\}$,\\
$\mathcal{R}_o=\{TastesHot, IsWhite, ContainsSpice, ContainsSugar\}$,
$\mathcal{F}_o=\{\}$.
\item The language of enquiry $\mathcal{L}$ is given by
$\mathcal{C}_o=\{$milk, curry, rice$\}$,
$\mathcal{R}_o=\{$TastesHot, IsWhite, ContainsSpice, ContainsSugar$\}$,
$\mathcal{F}_o=\{\}$.
\end{itemize}
(by the way, that's hardly a minimal example.)
Best Answer
One can eliminate the
\vspace*{-\baselineskip}from the other solution by using\abovedisplayskip=-\baselineskipinstead. Note thatequationuses\abovedisplayshortskip.