I am a little shocked that neither the blog post nor the twitter discussion nor any of the discussion here clearly identifies the missteps of this approach beyond alluding to a "category" or "type" error (which is correct, but not particularly informative.)

The issue here is around the semantics of the mathematical operators. It isn't even really about the types to which they apply; there are systems where `=` is well defined on heterogenous types.

The reason the answer to all these questions is a clear "no" is that they do not satisfy the core properties of the operators. For example, take equality. Equality in almost all mathematical constructs means that it supports substitution, is symmetric, transitive and reflexive. There are also well defined properties for the concepts of `greater than` and `less than`.

So, no, the OP's conclusion "Literally we’re all just making it up" is incorrect. You cannot use the operators `=`, `<`, and `>` between dates and times because they do not satisfy the core properties that define those operators. (I guess you could try to document an alternate definition of equality without the symmetric property in your documentation but... good luck with that not leading to massive confusion.)

Where you can just make it up is to define new operators as you actually want them to be. It's not `=`, it's `myDateTime=()` and then you're free to write the definition of that yourself. As long as you're consistent in the UI of how you present it (don't pretend it's vanilla `=` to the user!) you will at least be telling the truth. It may not solve all your problems but at least you won't be feeding any more to the fires of confusion, which you will as long as you keep pretending it's possible to make `=` mean something that's not reflexive.