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A comment on Alternative notation for exponents, logs and roots? (2011). Parent comment

Re:Alternative notation for exponents, logs and roots? (2011) by kortex on Wednesday December 02, 2020 @11:19AM (#25277836)
This really hammers home the advantage of this notation. It leads naturally to the question, "What is the operation when we leave the bottom right constant?" which Grant calls "O-plus" (tex call it \oplus), which is in fact related to the harmonic mean (which is n times the o-plus of the terms). I don't know if there's a better term for "o-plus" other than "reciprocal sum of reciprocals". Maybe "optical sum" which kind of makes o-plus make even more sense?

https://en.wikipedia.org/wiki/Optic_equation

https://en.wikipedia.org/wiki/List_of_sums_of_reciprocals

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Re:Alternative notation for exponents, logs and roots? (2011) by multidim on Wednesday December 02, 2020 @03:13PM (#25280956)
> which is in fact related to the harmonic mean (which is n times the o-plus of the terms). I don't know if there's a better term for "o-plus" other than "reciprocal sum of reciprocals"

I would call it the "harmonic norm", which is consistent with is being the "norm version" of the harmonic mean. It might also be called the "(p=-1) norm" since it would be a p-norm with p=-1. Also "L-1 norm" to put it in the "L norm" family.

https://en.wikipedia.org/wiki/Norm_(mathematics)#p-norm

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