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(Subscripts k and r are bracketed because they are superfluous, i.e., they are uniquely determined by county i).
On a superficial level, it seemed superfluous: I hadn't known many of them, and why would my sexuality matter to people whom I hadn't seen for a quarter century and might never see again?
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Googe said, "At the beginning I used to go down [to the studio] most days but after a while I began to feel pretty superfluous so I went down less".
While he quite liked 'Flip Ya Lid' by Nightmares On Wax, he was annoyed by its superfluous whistling: 'I'd buy their album as long as there's no other whistling on it.
"Only where the state ends, there begins the human being who is not superfluous" (Z I:11) Of course, it is only the latter individual that really interests Nietzsche.
I will spare you superfluous details -- I'm sure you've got your own challenges.
That superfluous and confusing "i" in his Christian name may already have given the game away.
The signs at the junction had been clear, but since then long stretches had gone by without any of the superfluous reassurance that I'd grown used to and now seemed to require.
Part of me feels that it's superfluous, and if I need to use rubber that is more important.
Perhaps like me you cherish the lingering question: Is this thing that I do superfluous?
Whether it was something as trivial as dipping too heavily into office supplies or free snacks, or a bolder gambit of convincing an employer to give me a "now superfluous" MacBook Pro as I moved on to another job, I have had a long career of getting shit for free that likely took root all those summers ago.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com