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fix: proofread Set Theory I part - #337

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Jul 9, 2026
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fix: proofread Set Theory I part#337
vEnhance merged 1 commit into
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claude/loving-clarke-269a5e

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@vEnhance vEnhance commented Jul 9, 2026

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This PR proofreads the Set Theory I: ZFC, Ordinals, and Cardinals part (issue #315), covering:

  • tex/set-theory/zorn-lemma.tex
  • tex/set-theory/zfc.tex
  • tex/set-theory/ordinal.tex
  • tex/set-theory/cardinal.tex

All the substantive mathematics checks out — the bijection tables ($\omega+1 \approx \omega$, $\omega \approx \omega^2$), ordinal/cardinal arithmetic constructions, the von Neumann hierarchy computations ($V_3 = {0,1,2,{1}}$), and the $\kappa \cdot \kappa = \kappa$ proof with its $<_{\max}$ enumeration table all verify correctly.

Only a few minor issues were found and fixed:

  • zfc.tex: stray comma in the Cantor diagonal exercise — "Show that if, $\iota$ exists," → "Show that if $\iota$ exists,".
  • zorn-lemma.tex: grammatical slip in the Cauchy functional-equation problem — "It's possible for $f$ is nonconstant …" → "It's possible that $f$ is nonconstant …", matching the phrasing of the adjacent item.
  • cardinal.tex: stray space inside a subscript, $\aleph_ 0$$\aleph_0$.
  • cardinal.tex: the example titled "Beth fixed point" actually concerns the aleph function ($\kappa = \aleph_{\aleph_{\aleph_\ddots}}$, so $\kappa = \aleph_\kappa$), not the beth function; retitled to "Aleph fixed point".

No large mathematical errors were found.

🤖 Generated with Claude Code

https://claude.ai/code/session_01JYnQwxZGUNjX354EBzZoRN


Generated by Claude Code

Minor corrections in the Set Theory I part (ZFC, Ordinals, Cardinals):

- zfc: fix stray comma in Cantor diagonal exercise ("if, $\iota$ exists")
- zorn-lemma: fix grammar in Cauchy FE problem statement
  ("possible for $f$ is nonconstant" -> "possible that $f$ is nonconstant")
- cardinal: remove stray space in subscript ($\aleph_ 0$ -> $\aleph_0$)
- cardinal: correct example title "Beth fixed point" -> "Aleph fixed point",
  since the example concerns the aleph function ($\kappa = \aleph_\kappa$),
  not the beth function

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01JYnQwxZGUNjX354EBzZoRN
@vEnhance vEnhance added the proofreading-campaign Systematic full proofreading of text label Jul 9, 2026 — with Claude
@vEnhance vEnhance mentioned this pull request Jul 9, 2026
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vEnhance merged commit d386b64 into main Jul 9, 2026
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