adherence value, extracted seq, limit point

[affeldt-aist]

Motivation for this change

Checklist

• [x] added corresponding entries in CHANGELOG_UNRELEASED.md

• [x] added corresponding documentation in the headers

Reference: How to document

Merge policy

As a rule of thumb:

• PRs with several commits that make sense individually and that all compile are preferentially merged into master.
• PRs with disorganized commits are very likely to be squash-rebased.

Reminder to reviewers

• Read this Checklist
• Put a milestone if possible
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[affeldt-aist]

Note that Bolzano-Weierstrass is a direct consequence of these lemmas.

[Tragicus]

Note that Bolzano-Weierstrass is a direct consequence of these lemmas.

How so?

[affeldt-aist]

Note that Bolzano-Weierstrass is a direct consequence of these lemmas.

How so?

it just lacks a lemma to extract a sequence from a sequence with a finite image:

https://github.com/math-comp/analysis/pull/1787/commits/36a05fe9f2a5b9747e192cc623bb9ded4ede45bd

[affeldt-aist]

Note that Bolzano-Weierstrass is a direct consequence of these lemmas.

How so?

it just lacks a lemma to extract a sequence from a sequence with a finite image:

36a05fe

and we'd like to have it in master to use it to prove the Heine-Cantor theorem (no PR yet)