Bug in `core.composition` comparison

[DanielYang59]

Bug in core.composition comparison

Open this in case it got forgotten.

As found out by @janosh in https://github.com/materialsproject/pymatgen/pull/3792#discussion_r1584003750, there is an obvious bug with Composition comparison where True is returned too early: https://github.com/materialsproject/pymatgen/blob/6c696cdb327621d5d16c675478f4ed0e024feea1/pymatgen/core/composition.py#L195-L212

On top of this obvious bug, there are a few questions:

• The docstring adds to ambiguity: (Should ONLY be used for defining a sort order (the behavior is probably not what you'd expect).).
• It appears that we don't need to sort this union set?
• How should we define the behavior when a Element is only in one of the Composition and this Composition is not a superset of another? For example:
  • Composition({"O": 1, "S": 1}) > Composition({"O": 1}) # This makes sense
  • Composition({"S": 1}) > Composition({"O": 1}) # This feels a bit weird though the atomic number is indeed greater
  • Composition({"O": 2, "N": 1}) > Composition({"O": 2, "C": 1}) # This doesn't seem to make sense? But this could be inferred by previous case (so should we prevent atom different Element from being compared altogether?).

https://github.com/materialsproject/pymatgen/blob/6c696cdb327621d5d16c675478f4ed0e024feea1/tests/core/test_composition.py#L504-L516