Issue 4395 is already open for the != delegating to __eq__ issue that Guido pointed out earlier.

Yet another issue that this doc patch should solve: Issue 22000.

I am posting v13 of the patch that works with the current “default” (3.5) branch. Minor modifications to the documentation part:

* Undo some paragraph reflowing to reduce the size of the diff hunks
* Use math.nan instead of nan = float('NaN')
* Tweaked the new subheadings to better differentiate “Value comparisons” (which this bug is concerned with) from “Identity comparisons”

Changes I made to the added test cases:

* Drop Python 3 version check
* Use TestCase.subTest() so it’s easier to see everything that [is] was failing
* Merge some tests for != and fix changed expectations due to Issue 21408 being fixed
* Drop _inst_str() and __str__(), apparently unused

It would be nice to see at least the documentation part reviewed and committed, even if the tests require more work. (After having to hack the tests to get them working, I might point out some odd bits in the code review.) Though I guess they are just tests, so it doesn’t matter so much as long as they pass.