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"impossibility of implementing" is correct and usable in written English.
You can use it when referring to the difficulty involved in carrying out a particular course of action. For example, "Due to the high costs, the impossibility of implementing such a policy means that it is not feasible".
Exact(5)
Even top down reformers with no awareness of realities within schools and systems should have anticipated the impossibility of implementing Common Core testing while also implementing value-added teacher evaluations.
The report, however, documented the practical impossibility of implementing the needed reforms as J.P. Morgan traders had proven their ability to hide losses from internal monitoring for months at a time, to breach bank-imposed risk limits, to manipulate risk evaluation models, and to "dodge or stonewall" regulatory oversight.
Given the impossibility of implementing the study as described, the tumor specimen was thus used for an in vitro autoradiographic study.
The major limitation in randomised trials of this sort is the impossibility of implementing blinding of the participants or field workers, once they visited the home.
However, apart from the impossibility of implementing a double-blind test for acupuncture, our viewpoint is to seek to determine the validity of clinical practices that are feasible in pragmatic contexts.
Similar(55)
An impossibility, of course.
Call it the impossibility of hope.
Rent and the impossibility of paying it.
"Doctor Who" is a chronicle of the impossibility of rescue.
Zeno's paradoxes purport to prove the impossibility of motion.
Yet she becomes aware of the impossibility of her task.
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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