If you want to say that floating point numbers are not ordered for exactly the same reason, and in exactly the same way, as sets... well, I guess you can die on that hill.  Since NaN is an IEEE-854 value, everything you mention is precisely identical of floats.

Is your argument that we need to stop using the '<' operator for floats also?!

On Thu, Dec 26, 2019 at 4:31 PM Marco Sulla via Python-ideas <python-ideas@python.org> wrote:
Andrew Barnert wrote:
> I didn’t want to get into that, because I assumed you weren’t going to argue that
> <= makes sense for sets but < doesn’t

So you're telling about **strict** partial ordering. I can spend thousand of words, but I think Python can speak for me:

```
(venv) marco@buzz:~/sources/tests/more_itertools\$ python3.9
Python 3.9.0a0 (heads/master-dirty:d8ca2354ed, Oct 30 2019, 20:25:01)
[GCC 9.2.1 20190909] on linux
>>> import random
>>> a = [set(), {1}, {2}, {3}, {1, 4}, {1, 4}, {3, 7}, {3, 7, 10}, {10}]
>>> random.shuffle(a)
>>> sorted(a)
[set(), {3}, {10, 3, 7}, {2}, {1, 4}, {10}, {3, 7}, {1}, {1, 4}]
>>> random.shuffle(a)
>>> sorted(a)
[set(), {3, 7}, {1}, {10}, {3}, {10, 3, 7}, {1, 4}, {1, 4}, {2}]
>>> random.shuffle(a)
>>> sorted(a)
[set(), {3, 7}, {1}, {10}, {3}, {1, 4}, {1, 4}, {10, 3, 7}, {2}]
>>> random.shuffle(a)
>>> sorted(a)
[set(), {1}, {10}, {3}, {2}, {3, 7}, {10, 3, 7}, {1, 4}, {1, 4}]
>>> random.shuffle(a)
>>> sorted(a)
[set(), {2}, {3, 7}, {1}, {1, 4}, {10}, {3}, {10, 3, 7}, {1, 4}]
```

Notice the positions of the two {1, 4} sets......

SOooooo.... sorted(sets) does **not** sort at all. Total, partial, so and so, nothing.

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