But if someone wanted to write a user-defined division function or operator that would return Inf for (anything > 0) / 0 and for (anything < 0) / -0, and -Inf for (anything < 0) / 0 and for (anything > 0) / -0, and NaN for (either zero) / (either zero), I think that function or operator would be fully in keeping with IEEE 754.
Upon further reading you are correct - IEEE 754 has chosen to treat n/0 differently for n=0 and n<>0 cases. I'm sure they have their reasons but within the scope of this database, and the core arithmetic functions it provides, those distinctions don't seeming meaningful and having to add query logic to deal with both cases would just be annoying. I don't use, or have time for the distraction, to understand why such a decision was made and how it could be useful. Going from an exception to NaN makes sense to me, going instead to infinity - outside of limit expressions which aren't applicable here - does not.
For my part in the queries I have that encounter divide-by-zero I end up transforming the result to zero which is considerably easier to present/absorb along side other valid fractions in a table or chart.
