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The phrase "is extremely arbitrary" is correct and usable in written English.
It can be used to describe a decision, rule, or action that seems random or lacking in reason or fairness. Example: "The selection process for the award is extremely arbitrary, leaving many deserving candidates overlooked."
Exact(3)
Clearly, Ms. Prose's choice of muses in this book is extremely arbitrary.
What's more, "True Believers" is extremely arbitrary in what it leaves in and what it leaves out.
In fact, the situation is extremely arbitrary.
Similar(56)
Especially in the US, clothing sizes can be extremely arbitrary and not standard from designer to designer.
It is exceedingly arbitrary.
In case of models with arbitrary topology, it is extremely difficult to maintain continuity conditions among neighboring surfaces.
Deadlock detection in concurrent programs that create networks with arbitrary numbers of nodes is extremely complex and solutions either give imprecise answers or do not scale.
Just like any other biological experiments, it is extremely difficult to exclude false positives without creating false negatives and to set an arbitrary but significant threshold.
STEM is also extremely arbitrary -- while business-related disciplines such as Econometrics, Business Statistics, and Management Science are included in STEM, an MBA is excluded.
The basal LDL oxidation (as defined in Materials and Methods) was extremely low and was arbitrary assigned 100%% value.
This unity seems to be extremely precarious and ultimately grounded in the arbitrary acts of a pro-physical subject.
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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