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fix: disambiguate duplicate Verso labels in Section 5.3 - #652

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Chessing234:fix/section-5-3-verso-labels
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fix: disambiguate duplicate Verso labels in Section 5.3#652
Chessing234 wants to merge 2 commits into
teorth:mainfrom
Chessing234:fix/section-5-3-verso-labels

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@Chessing234

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Section 5.3 has five groups of declarations sharing one docstring:

  • Proposition 5.3.3 / Exercise 5.3.1 — 2
  • Definition 5.3.1 (Real numbers) — 2
  • Definition 5.3.4 (Addition of reals) — 2
  • Proposition 5.3.11 (laws of algebra) — 4 instances
  • Examples 5.3.13 — 5 examples

Definitions and propositions fold the part into the parenthetical (as in #624); the five examples take part letters (as in #634 for Examples 5.2.2). Docstrings only.

Checked: no duplicate one-line docstrings remain in the file, all edited lines within 100 characters.

lake build Analysis.Section_5_3 succeeds locally — ✔ [3268/3268] Built Analysis.Section_5_3 (103s), Build completed successfully.

Fifteen docstrings across five groups shared a label: Proposition 5.3.3,
Definition 5.3.1, Definition 5.3.4, Proposition 5.3.11 and Examples 5.3.13.
The definitions and propositions fold the part into the parenthetical; the
five examples take part letters, as in Examples 5.2.2.
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Thanks — most of this is exactly right, and I've merged the sibling PRs (#651, #653, #655, #656, #657, #659, #660, #661) that use the same descriptive style.

One change here I'd like adjusted before merging. The Examples 5.3.13 block is prose in the text, not an enumerated list — ch5 reads:

The sequence $1$, $-1$, $1$, $-1$, ... is bounded away from zero (all the coefficients have absolute value at least 1). But the sequence $0.1, 0.01, 0.001, \dots$ is not bounded away from zero, and neither is $0, 0.9, 0.99, 0.999, \dots$. The sequence $10, 100, 1000, \dots$ is bounded away from zero, but is not bounded.

So there are no parts (a)–(e) to refer to; adding them makes the docstring claim a structure the book doesn't have, and a reader who goes looking for "Examples 5.3.13(c)" won't find it. Could you use the same descriptive parentheticals you've used everywhere else in this PR? Something like:

  • Examples 5.3.13 (alternating signs)
  • Examples 5.3.13 (decaying powers of ten)
  • Examples 5.3.13 (approaching one from below)
  • Examples 5.3.13 (growing powers of ten, bounded away from zero)
  • Examples 5.3.13 (growing powers of ten, not bounded)

Everything else in the PR is good to go as-is.

The book's Examples 5.3.13 is a single prose paragraph with no
enumerated parts, so (a)-(e) claimed a structure the text does not
have. Replace them with the descriptive parentheticals used for the
other labels in this PR.
@Chessing234

Chessing234 commented Aug 24, 2026

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Done in 0248c0d — the five Examples 5.3.13 labels now use your suggested parentheticals: (alternating signs), (decaying powers of ten), (approaching one from below), (growing powers of ten, bounded away from zero), (growing powers of ten, not bounded). Nothing else changed.

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@Chessing234@teorth