[issue39862] Why are the union relationships not implemented by default for ≤ and ≥?

[Géry]

Géry <gery.ogam at gmail.com> added the comment:

More precisely:

The following relationships are always valid and therefore implemented by default in Python (_except for the union relationships, which seems arbitrary and is the reason of this Python issue_):

- 2 [complementary](https://en.wikipedia.org/wiki/Binary_relation#Complement) relationships: "= and ≠ are each other’s complement";
- 6 [converse](https://en.wikipedia.org/wiki/Binary_relation#Converse) relationships*: "= is the converse of itself", "≠ is the converse of itself", "< and > are each other’s converse", and "≤ and ≥ are each other’s converse";
- 2 [union](https://en.wikipedia.org/wiki/Binary_relation#Union) relationships: "≤ is the union < and =" and "≥ is the union of > and ≤".

The following relationships are only valid for [total orders](https://en.wikipedia.org/wiki/Binary_relation#Properties) and therefore not implemented by default in Python (but users can conveniently implement them when they are valid with the [`functools.total_ordering`](https://docs.python.org/3/library/functools.html#functools.total_ordering) class decorator provided by the Python standard library):

- 4 [complementary](https://en.wikipedia.org/wiki/Binary_relation#Complement) relationships: "< and ≥ are each other’s complement" and "> and ≤ are each other’s complement".

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\* Converse relationships are implemented in Python through the [`NotImplemented` protocol](https://docs.python.org/3/reference/datamodel.html#the-standard-type-hierarchy).

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Python tracker <report at bugs.python.org>
<https://bugs.python.org/issue39862>
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