[Merged by Bors] - feat(analysis/normed/field/basic): define densely_normed_field give instances for ℚ, ℝ, ℂ and is_R_or_C
#15657
Conversation
This file contains 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
j-loreaux
added
awaiting-CI
github-actions
bot
removed
the
awaiting-CI
4 tasks
|
✌️ j-loreaux can now approve this pull request. To approve and merge a pull request, simply reply with |
leanprover-community-bot-assistant
added
delegated
Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr>
|
bors r+ |
bors bot
pushed a commit
that referenced
this pull request
Aug 9, 2022
… instances for ℚ, ℝ, ℂ and `is_R_or_C` (#15657) This adds a new type class extending `normed_field` which is named `densely_normed_field` per this [Zulip discussion](https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/hypotheses.20for.20a.20field.20property/near/290408091). The name comes from the fact that the (nn)norm has dense range in ℝ≥0. This type class is strictly stronger than `nontrivially_normed_field`, with `padic` being a field which is nontrivially normed but not densely normed. The instances of `nontrivially_normed_field` for each of ℚ, ℝ, ℂ have all been migrated to `densely_normed_field` instead. Moreover, `is_R_or_C` now extends `densely_normed_field`; this is natural because even if it only extends `nontrivially_normed_field`, it would still be possible to prove that the norm has dense range in ℝ≥0.
|
Pull request successfully merged into master. Build succeeded: |
bors
bot
changed the title
densely_normed_field give instances for ℚ, ℝ, ℂ and is_R_or_Cdensely_normed_field give instances for ℚ, ℝ, ℂ and is_R_or_C
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
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Outdated suggestions cannot be applied.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.
This adds a new type class extending
normed_fieldwhich is nameddensely_normed_fieldper this Zulip discussion. The name comes from the fact that the (nn)norm has dense range in ℝ≥0. This type class is strictly stronger thannontrivially_normed_field, withpadicbeing a field which is nontrivially normed but not densely normed.The instances of
nontrivially_normed_fieldfor each of ℚ, ℝ, ℂ have all been migrated todensely_normed_fieldinstead. Moreover,is_R_or_Cnow extendsdensely_normed_field; this is natural because even if it only extendsnontrivially_normed_field, it would still be possible to prove that the norm has dense range in ℝ≥0.