Rewrite the first example of the amsmath subsection

[marmotghost]

The first example in the amsmath subsection is unfortunate in a few ways. Please consider rewriting it as

\documentclass{article}
\usepackage{amsmath}

\begin{document}
Given  $n,k\geq 0$, solve the recurrence for
\begin{align*}
  Q_{n,0} &= 1   \quad Q_{0,k} = [k=0]\;;  \\
  Q_{n,k} &= Q_{n-1,k}+Q_{n-1,k-1}+\binom{n}{k} \quad\text{for $n$, $k>0$.}
\end{align*}
\end{document}

This avoids the colon before the displayed equations, which is sometimes said to be bad style, and, more importantly introduces spacing before punctuation in formulas in displayed equations. Why is that necessary? Here is why.

\documentclass{article}
\usepackage{amsmath}

\begin{document}
\begin{align*}
  R_{ij'} &= T_{ij},\\
  \widetilde{R}_{ij'} &= \widetilde{R}_{ij}. \tag{bad}
\end{align*}
\begin{align*}
  R_{ij'} &= T_{ij}\;,\\
  \widetilde{R}_{ij'} &= \widetilde{R}_{ij}\;. \tag{better}
\end{align*}
\end{document}

Punctuation close to some formula has repeatedly lead to confusion, e.g. $T_{ij},$ is hard to distinguish from $T_{ij'}$, and there are many more examples of this kind.

[car222222]

Maybe more generally the math examples should be carefully scrutinized by a talented math editor?

[josephwright]

Maybe more generally the math examples should be carefully scrutinized by a talented math editor?

Suggestions?

[car222222]

If the scrutineer must know about so very many things, such as the 'standard conventions' in (some) science and (all?) engineering disciplines and about all typesetting cultures and regimes for abstraction of mathematical input . . .
then no, no suggestions at all!!

[car222222]

Maybe, along with translations to other languages, we also need translations to each of the many 'languages' that are more commonly called 'the traditions, conventions and trade-craft used by different clans of mathematical authors/editors/typesetters/etc.' ???

[davidcarlisle]

I suggest we leave this unchanged.

Personally I don't mind the colon before the display.

I have a mild preference for adding space before end of display punctuation, but it is by no means universal practice to add space there. The space commands are the specific subject of the following lesson so adding them at this point would probably need a forward reference and give them more prominence than you want here when the point of the example is alignment.