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The phrase "a task impossible" is correct and usable in written English
You can use this phrase to emphasize the difficulty or impossibility of something. For example: "The professor assigned us a task impossible – solve a 500-year-old mathematical equation!"
Exact(4)
He and his superiors attempted to suppress buccaneering, a task impossible without adequate naval patrols.
Given the sheer crush of news releases, wire services do not generally verify their authenticity, a task impossible under current competitive pressures.
Further, we find that dual homeostatic control naturally preserves both the mean and the variance of the firing rate, a task impossible for a homeostatic system with a single slow feedback mechanism.
The Chief of the Air Staff, Air Vice Marshal George Jones, in recommending Goble's dismissal, wrote that "this officer has a sound Service knowledge and an alert mind, but suffers from certain nervous characteristics which make continuous application to a task impossible".
Similar(53)
Using a group of participants with very mixed first language (L1) backgrounds was not possible because it would have made the use of a translation task impossible.
Yet, translation into effective therapies is even more challenging than sequencing--a task considered impossible less than 30 years ago.
Was his task impossible?
"It is a Sisyphean task, an impossible task in some senses.
Such a task is clearly impossible.
It was an uphill task, an impossible task.
Isn't this film a bit of an impossible task then?
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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