Bad case.
Pick h defined as 1/0 s.t. 0 * h = 1
anyways that's just some basic motivation for Hitomi analysis.
What you've shown is worse than Hitomi analysis, which has similar and more precise conclusions.
I highly recommend you read into Hitomi analysis.
If you like what's in the OP I think you will really like the crux problem.
Here's an important question you should ask yourself: what can you say about that infinity?