Skip to content

fix: refute Ex. 9.8.4 without StrictMono; label §6.3 examples - #628

Closed
Chessing234 wants to merge 3 commits into
teorth:mainfrom
Chessing234:fix/ex-9-8-4-false-and-6-3-labels
Closed

fix: refute Ex. 9.8.4 without StrictMono; label §6.3 examples#628
Chessing234 wants to merge 3 commits into
teorth:mainfrom
Chessing234:fix/ex-9-8-4-false-and-6-3-labels

Conversation

@Chessing234

Copy link
Copy Markdown
Contributor

Summary

  • Prove Exercise 9.8.4 without strict monotonicity is false (apply isFalse): constant f ≡ 0 on [0,1] is continuous and monotone but admits no left inverse
  • Disambiguate duplicate Verso labels for Examples 6.3.3–6.3.5 and Remark 6.3.7

Test plan

  • lake build Analysis.Section_9_8
  • lake build Analysis.Section_6_3

A constant continuous monotone map on [0,1] has no left inverse, so
Exercise 9.8.4 without StrictMonoOn is false.

Signed-off-by: Taksh <takshkothari09@gmail.com>
Split duplicate Verso labels into (a)/(b)/(c) parts so doc references
stay unique.

Signed-off-by: Taksh <takshkothari09@gmail.com>
@Chessing234

Copy link
Copy Markdown
Contributor Author

ex 9.8.4 false-sorry + §6.3 labels are on tip; happy to split if you'd rather land labels separately.

@teorth

teorth commented Aug 3, 2026

Copy link
Copy Markdown
Owner

The Section 6.3 half of this is good and I would happily take it — but the Analysis/Section_9_8.lean hunk discharges the sorry in MonotoneOn.exist_inverse_without_strictmono with a full apply isFalse; … proof, and the repository deliberately does not carry solutions to the Analysis I exercises:

README.md — "Readers are welcome to fork the repository here to try their hand at these exercises, but I do not intend to place solutions in this repository directly."

Note that the line you replaced was the hint left for the reader (-- apply isFalse: e.g. a constant monotone f on [a,b] has no strict inverse), which is exactly the part the exercise is asking them to supply.

Please do resubmit the Section 6.3 labels on their ownExample 6.3.3/6.3.4/6.3.5 (a)/(b) and Remark 6.3.7 (a)/(b)/(c). I checked those against the text: Examples 6.3.3–6.3.5 are each a single prose example asserting a sup and an inf, and Remark 6.3.7 is the dual of the three claims of Proposition 6.3.6, so the counts line up and lettered parts match the convention the book uses predominantly. That half would merge as-is. (#627, which labels Propositions 6.3.6/6.3.8 and Example 6.3.9 in the same file, has just been merged, so it will need a rebase.)

Analysis/MeasureTheory/ is the exception to the solutions policy — its README says "Readers who are not in my classes are also welcome to submit such proofs." The restriction is only on the Analysis I sections.

@teorth teorth closed this Aug 3, 2026
@Chessing234

Chessing234 commented Aug 4, 2026

Copy link
Copy Markdown
Contributor Author

resubmitted the §6.3 labels alone as #633 (no 9.8.4 solution).

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment

Labels

None yet

Projects

None yet

Development

Successfully merging this pull request may close these issues.

2 participants