Quite the opposite I would say: the harmonic mean can be seen as a very good justification for `1/0=inf` as the pragmatic choice. If, say, `a` is mathematicall

Quite the opposite I would say: the harmonic mean can be seen as a very good justification for `1/0=inf` as the pragmatic choice. If, say, `a` is mathematically very small (and `x` is accordingly expected very small`) but `a` become zero due to rounding behavior, then having `1/a=inf` results in `x=0` which is arguably closer to the expected result than e.g. `x=2b`. As someone involved with numerical methods, I have very often relied on `1/0=inf` because it would ultimately warrant the proper behavior in case of rounding errors in the denominator.