If I write a UniqueNumber that just returns false on the == operator, I'd be stupid but the hash map should still work. Java has a separate getHashCode() and equals() method for a reason.
Either provide a hash key override or use the raw bits for deep compares. Custom equality algorithms usually don't make sense for arbitrary key-value stores.
In Rust you can make UniqueNumber, indeed misfortunate::OnewayGreater is such a type. misfortunate::Maxwell even more so.
However of course the HashMap can't meaningfully "work" for this type. Rust promises your program doesn't have Undefined Behaviour despite such a prank, but it might spin forever when you try to insert this type into a map for example, a well defined but undesirable behaviour brought on by your poor choices.
You seem to imagine that Java's hash map doesn't need to compare types, that it can just use getHashCode() -- however because of the Pigeonhole Principle that can't actually work.
And NaN != NaN isn't a "custom equality algorithm" it's literally how the floating point numbers are defined in your CPU.
if (p.hash == hash &&
((k = p.key) == key || (key != null && key.equals(k))))
NaN's work in a Java hashmap because Float.hashCode returns floatToIntBits(float) which normalizes all NaN's to a canonical value.
Rust has a magic unstable trait StructuralEq which means not only are we promised that values of this type can be compared for equality (that's what Eq does) but that comparison will just be a bitwise memory comparison. Lots of useful things are not StructuralEq even if they are Eq
Apparently Java's Floats also do the same canonicalisation for equals(). So in effect in Java although NaN != NaN, once you box it that ceases to be true. This seems like a spectacularly bad idea to me, but presumably it made somebody's awful hack work at one point.
but elsewhere you say, "You are welcome to build a type which has this property and declares that it is Eq". This is exactly the difference between double and Double in Java. double has the `==` operator that isn't reflexive and works as required by IEEE-754 and Double has Double.equals, which is documented[1] to be a reflexive, transitive, symmetric, consistent, and substitutable relation.
[1]: https://docs.oracle.com/en/java/javase/17/docs/api/java.base...
In my opinion, language native hash maps should operate on memory, not on types and their weird implementations. Negative zero and positive zero are defined as different values but are mathematically equal; however, math functions may (and in the case of C, do) behave differently depending on which one you use. Even in higher level languages such as Java sorting gets affected by the presence of negative and positive zero using min/max operators.
If two values claim equality but do effectively alter program behaviour, I consider their equality operation in the context of memory operations such as hash maps to be buggy. There are good reasons to rely on the equality operators, but I do not think such behaviour should be the default.