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"impossibility of a" is correct and usable in written English.
It is typically used to introduce a subject that is not achievable or attainable. For example: "Given the current circumstances, the impossibility of a successful resolution is becoming increasingly clear."
Exact(60)
It seems the impossibility of a deal with Labour became increasingly apparent as the day progressed.
I could have quoted every verse in there, especially those beautiful passages about the impossibility of a dream.
However, it seems that Lib Dem MPs themselves were realising the impossibility of a Lib-Lab pact.
Is this appointment, in fact, that holy grail – final confirmation of the physical impossibility of a female DG?
The necessity and impossibility of a true partnership with the Karzai regime is the central contradiction in our Afghanistan policy.
Chelsea suddenly required the impossibility of a further three goals to redeem themselves in this semi-final.
Critics will point to this as further evidence of the impossibility of a direct transplant from private to public sectors.
But "Don't be evil" also represents the impossibility of a more nuanced social code, a problem faced by many Internet companies.
With the Obama family in the White House, what once seemed the impossibility of a black president is defied visually every day.
These books, which have a close connection with the biblical Book of Daniel, stress the impossibility of a rational solution to the problem of theodicy.
In the dramas of Athens and England, tragedy was born of the impossibility of a clear-cut victory in the human struggle with powers greater than oneself.
More suggestions(25)
impossibility of a true
impossibility of a priori
impossibility of an agreement
impossibility of a fair
impossibility of a definitive
impossibility of a sequence
impotence of a
shortcoming of a
powerlessness of a
aberration of a
ability of a
flaw of a
incapacity of a
refusal of a
lack of a
fragility of a
unavailability of a
weakness of a
inability of a
failure of a
helplessness of a
impediment of a
absence of a
denial of a
hopeless of a
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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