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.
Re:1/0 = 0
by Veedrac on Saturday August 11, 2018 @05:47AM
(#17739050)
I think for floating point 1/0=Inf makes a lot of sense, because divisions are frequently done with continuously-varying properties. Division by integers is different, since you do a different kind of work with it; there is no "very small" integer.
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.