Authoring

Reference for writing content on this site. This page is also the live test of every custom shortcode — if something here renders wrong, the shortcode is broken.

Front matter

Pages use TOML front matter delimited by +++.

+++
title = 'Limits and Continuity'
description = 'One sentence, shown in section listings and search results.'
weight = 30
chapter = 2
+++

Start new pages from an archetype rather than by hand:

hugo new content books/calculus/limits.md

hugo new content books/calculus/_index.md --kind chapter

Mathematics

Write LaTeX directly. $...$ is inline, $$...$$ is displayed, and MathJax loads on every page.

The Euler identity $e^{i\pi} + 1 = 0$ sits inline in the sentence. A displayed equation gets its own line:

Long displayed equations scroll within their own box rather than forcing the whole page sideways on a phone.

Because Goldmark passes $...$ through untouched, backslashes and underscores inside mathematics need no escaping: $a_1 + a_2$ gives $a_1 + a_2$, not italics.

When to reach for LaTeX at all: regular prose stays plain Markdown even on a heavily mathematical page — LaTeX is for the actual objects, not the discussion around them. A variable, proposition, set, or function gets inline math the moment it’s referenced, even as a single bare letter ($p$, not “p”). A full statement being presented as a proposition — not just mentioned — gets typeset whole via \text{} inside a math environment:

$$\text{Squares have four equal sides.}$$

or, when several need to line up together:

\[
\begin{array}{ll}
w\text{: H}_2\text{O is a liquid at 70 degrees Fahrenheit and 1 atmosphere.} &\text{(true)} \\
x\text{: 12 is divisible by 3.}                                             &\text{(true)}
\end{array}
\]

See content/books/foundational-mathematics/logic/propositions/_index.md for this pattern in full. Full rationale is in this project’s CLAUDE.md.

Statements

statement renders a numbered definition, theorem, example, or proof. The body is parsed as Markdown, so mathematics and emphasis work inside it:

{{< statement kind="theorem" name="Fundamental Theorem of Calculus" >}}
If $f$ is continuous on $[a, b]$ and $F$ is any antiderivative of $f$, then
$$\int_a^b f(x)\,dx = F(b) - F(a).$$
{{< /statement >}}

Which renders as:

Parameters

Numbering

Every numbered kind shares one counter per page, so a page reads Definition 1, Theorem 2, Example 3. That is the usual textbook convention, and it keeps a cross-reference unambiguous without having to name its kind.

Set the page’s chapter front matter to prefix numbers with the chapter — chapter = 3 gives Theorem 3.2.

Proofs and remarks are never numbered; a proof belongs to the statement above it.

Figures

Figures are pre-rendered SVGs committed to the repository. The site build never runs Asymptote, so deploying needs neither Asymptote nor LaTeX installed.

Keep the .asy source and its .svg output together in the page bundle:

content/books/calculus/riemann-sums/
├── index.md
├── left-sum.asy
└── left-sum.svg

Then reference the SVG by name:

{{< figure src="left-sum.svg"
           title="Figure 1:"
           caption="A left Riemann sum for $f(x) = x^2$."
           source="left-sum.asy" >}}

Passing source puts an Asymptote source disclosure under the figure — worth doing on any figure a reader might want to adapt. There is a live example on the Asymptote Library page.

A missing src or source fails the build rather than rendering a broken image.

Re-rendering

After editing any .asy under content/:

scripts/render-figures.sh

That renders only sources whose SVG is missing or older than the source. Pass --force to re-render everything, which you want after changing the library’s theme file.

Notice types

Every book uses the same six notice boxes, always — see /style-guide for what each one looks like and means to a reader; this section is the syntax reference for writing them. Full detail, including why term-highlighting is ==mark== syntax instead of a shortcode, is in this project’s CLAUDE.md.

All eight shortcodes (definition, theorem, proof, example, star, warning, question, answer) use the angle-bracket delimiter, never percent:

{{< definition terms="prime number" >}}
A natural number greater than 1 with no positive divisors other than 1 and
itself.
{{< /definition >}}

theorem, example, and star take a required title — a sentence fragment, not a number, e.g. title="Every prime greater than 2 is odd". definition takes terms — a comma-separated list, natural case; the box capitalizes them itself. question takes no parameters — it numbers itself.

theorem and example both number themselves — Theorem <chapter>.<section>.<n> and Example <chapter>.<section>.<n> respectively — where n restarts at 1 on every page, counted separately per type, and chapter/section come from the page’s own front matter (see the table above) — set neither and it’s just Theorem 1 / Example 1. Your title param supplies only the text after the number; you never write the number yourself:

{{< example title="Tossing two fair six-sided dice" >}}

renders as Example 2.1.3: Tossing two fair six-sided dice if it’s the third example on a page whose front matter sets chapter = 2 and section = 1.

proof takes no parameters and must come immediately after the theorem it belongs to; it reuses that theorem’s exact number rather than counting itself, so never put another theorem between a theorem and its proof:

{{< theorem title="Every prime greater than 2 is odd" >}}
If $p$ is prime and $p > 2$, then $p$ is odd.
{{< /theorem >}}
{{< proof >}}
Suppose, for contradiction, that $p$ is even. Then...
{{< /proof >}}

question/answer work the same way — answer immediately after the question it solves, reusing its number exactly like proof reuses theorem’s — except question numbers only itself (Question 1, Question 2, …), with no chapter or section prefix, so the pair reads Question 1 / Solution 1.

Highlight the term being defined inside a definition box by wrapping it in ==double equals signs==. Reserve this for that one context — don’t use it elsewhere on the page, even to name a rule or technique introduced outside a definition box (Modus Ponens, a direct proof, and so on); use **bold** for that instead.

Theme asides

The theme’s own notice shortcode is unrelated to the notice types above — it covers generic asides that don’t fit any of the six: