Section 11.5: correct Exercise 11.5.1 continuity statement - #620
Closed
teorth wants to merge 1 commit into
Closed
Conversation
`fun x ↦ 1/x` is not continuous on `Icc 0 1`: with Lean's `1/0 = 0`, the function fails to be continuous at `0` within the interval, so the stated `ContinuousOn` goal was false and the `sorry` unprovable. Negate it, matching the exercise's intent that Corollary 11.5.2 does not apply here. Also label both parts as Exercise 11.5.1, which they previously lacked. Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
2 tasks
Owner
Author
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
1 participant
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Extracted from #617, which also carried unrelated docstring changes.
example : ContinuousOn (fun x:ℝ ↦ 1/x) (Icc 0 1)was false, so thesorrywas unprovable: with Lean's1/0 = 0the function is discontinuous at0withinIcc 0 1. Negating it matches the exercise's intent — the point of Exercise 11.5.1 is that Corollary 11.5.2 does not apply, and that1/xis not Riemann integrable there either.Also adds the
Exercise 11.5.1docstring label to both parts, which they lacked.Credit to @Chessing234, who spotted this in #617.