[d-morrison]

This is the first PR in the mds/mcs consolidation that Ezra approved on 2026-11-02. It moves four general definitions out of the mcs CSCI 201 notes and into mds, and adds an example after each one. A later mcs PR will include them from here.

The floor function and the logarithm to base b were split out into Morrison-Lab/mds#566 to keep this PR under the size cap.

What changes

All of the definitions below go on the number-systems page.

• def-factorial and exm-factorial. The factorial is defined for non-negative integers, and the definition states that 0! = 1, which the mcs version left undefined.
• A new section, "Divisibility, primes and congruence", holds def-divides, def-prime and def-congruence, each followed by an example.
• The intro remark lists the new definitions.
• references.bib gets three Wikipedia entries copied from mcs.

The ids are the same as in mcs, so existing links in mcs keep working once mcs switches to these includes.

Two mcs theorems are held back for a follow-up: infinitely many primes, and √2 is irrational. Their proofs cite mcs remarks and an mcs exercise solution, so those have to move first.

Checks

• number-systems.qmd renders to HTML with no warnings.
• check-term-links, check-new-line-breaks and check-exm-figures pass locally against origin/main.

🤖 Generated with Claude Code

https://claude.ai/code/session_019xfc9pMBq15Hq3DgNBx1ox

[d-morrison]

Here is how each point from the review was handled. The new head is 6b02717.

1. Missing examples: fixed. Every new definition in this PR is now followed by an #exm- div. Each one lists single values, so it carries a no-figure note.
2. Semantic line breaks: fixed. _def-factorial.qmd now breaks at each clause, and the intro remark was rewritten. The floor and logarithm lines the review cited moved to #566, where they are also split.
3. Two terms in one div: kept as written. The review itself calls this borderline. ∤ and ≢ are notation for the negation of the relation the div defines. They are not separate terms, so they stay in that relation's div.

Suggestions:

• Logarithm uniqueness: handled in Add the floor function and the logarithm to base b #566, where rem-logarithm-formula derives log_b x = ln x / ln b.
• Linking the empty-product convention: not done. mds has no definition of an empty product to link to, so the one sentence states the convention instead.
• Adding composite numbers: not done, because it would be a new term with nothing in this PR that uses it.

The floor and the logarithm moved to #566 to keep this PR under the size cap.

Posted by Claude Code (AI agent) --- not written by a human.

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[github-actions]

PR Preview Action v1.8.1
🚀 Preview available at: https://Morrison-Lab.github.io/mds/pr-preview/pr-565/

_{Built to branch gh-pages at 2026-11-03 00:06 UTC.}

[github-actions]

Claude finished review — View run

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Re-reviewed e3de9b6, the only new commit since d8d27665. It replaces trailing (@def-...) crossrefs with linked terms in seven number-systems subfiles. I found no issues.

• Anchors: every link target exists. #def-divides, #def-nonnegative-integers, #def-positive-integer, #def-integers, #def-congruence, #def-prime and #def-factorial are each defined in a subfile.
• Math: the changed math lines only rearrange wording around existing \mid, \equiv and \factorial{} notation. They add no literal-letter, raw-operator or hat/tilde violations. The macro check does not apply to this diff beyond that.
• Prime definition: the old and new wording are equivalent. "No positive integer other than 1 and n divides it" is the same as "its only positive divisors are 1 and n". The new wording also links "positive integer" and "divides" at first use in the div.
• Semantic line breaks: each changed prose line holds at most one clause, or a short appositive such as ", written $n \mid (a - b)$,". I did not find a clause-level violation.
• Scope: only the crossref style changes. No ids moved, no content was added, and no generated files were touched.

The prior verdict, from the 2026-11-03T00:08 review of d8d27665, still stands.

Verdict

Ready for merge.

Structured Review Data (JSON)

{
  "schema_version": "1.1",
  "reviewer": "claude",
  "commit_sha": "e3de9b66603670c5e1dd6bfebef4443a5c2d9f6f",
  "verdict": "CLEAN",
  "findings": [],
  "detailed_assessment": "Seven number-systems subfiles swap trailing (@def-id) crossrefs for linked terms; every target id (divides, integers, positive-integer, nonnegative-integers, congruence, prime, factorial) is defined, and the prime definition wording is logically equivalent.",
  "holistic_assessment": "The change is scoped to crossref style, preserves ids and meaning, adds no math or generated-file changes, and does not alter the earlier clean verdict."
}

Reviewed commit: e3de9b6

[github-actions]

💰 Cost: $0.1907 (review) — run