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The phrase "arbitrary amount of time" is correct and usable in written English.
It can be used when referring to a time period that is not fixed or predetermined, often implying flexibility or randomness.
Example: "The project can take an arbitrary amount of time to complete, depending on the resources available."
Alternatives: "indefinite period of time" or "unspecified duration".
Exact(2)
Don't give yourself an arbitrary amount of time to get ready.
17 Similarly, for binocular rivalry, von Helmholtz 17 states that he could exert attentional control to keep one pattern dominant an "arbitrary" amount of time for a simple line stimulus and by performing a task (e.g., counting) with the respective percept for more complex patterns.
Similar(58)
No matter where a given species evolved in the first place, its inherited functional abilities may allow it to survive in a variety of places under a variety of conditions through arbitrary amounts of time, and in association with other species.
It usually involves taking a large jar or money box (something you can't easily break into) to which you will add a dollar (or some other arbitrary amount of money) every time you utter a swear word.
To evaluate loss of Bem1-GEF from the peak, we started with an arbitrary amount of Cdc42-Bem1-GEF, and ran simulations to monitor the loss of Bem1-GEF from the membrane over time, for different values of GTP-Cdc42.
To support integration with the real-time controller, the planner can provide useful advice when it is interrupted after an arbitrary amount of computation.
Restitution in mapping models with an arbitrary amount of memory.
The Xoom's arbitrary amount of fame was over months ago.
The Internal Revenue Service has approved an arbitrary amount of 31.5 cents per mile for travel reimbursement.
An arbitrary amount of metadata can be added to each genome.
An arbitrary amount of data from different platforms can be inspected, using the 'integrate heterogenous data' procedure.
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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