The phrase "a single impossibility" is correct and usable in written English.
It can be used to refer to one specific situation or event that is deemed impossible.
Example: "In the face of overwhelming odds, the team focused on overcoming a single impossibility that stood in their way."
Alternatives: "one sole impossibility" or "a lone impossibility".
The four volumes (1952 61) about the Borrowers, with their brief pendant, Poor Stainless (1971), ask the reader to accept only a single impossibility, that in a quiet country house, under the grandfather clock, live the tiny Clock family: Pod, Homily, and their daughter Arrietty.
In Dunn and Zhou 2005 only a single negation as impossibility is used, the vocabulary is enriched by conjunction and disjunction, and in both, the one with negation, conjunction, and disjunction as well as the one with negation only, subminimal negations are referred to as preminimal negations.
To accommodate more than that on the same channel, the microphones would have to be about 1,000 feet apart, an impossibility within a single theater, and essentially ruling out most nearby theaters.
And at a House Financial Services Committee hearing last week, during a confrontation with JPMorgan Chase chief executive Jamie Dimon, Porter assailed the bank's low wages by describing the impossibility of a single mom with a 6-year-old child trying to survive on an entry-level salary.
Dale Tuggy objects that a priori arguments for a Trinity of divine selves, like those of Swinburne, Stephen T. Davis, and Richard of St. Victor (d. 1173) fail to show the impossibility of a single perfect self (Tuggy 2013c; Richard of St. Victor 1979; also see section 2.5 below).
Cyber-attacks are difficult to prevent, given the relative ease with which hackers can find a single system vulnerability, and the impossibility of plugging every conceivable security hole.
The different demises of the Wicked Priest and the tenses associated with them are often cited as evidence of the impossibility of a single Wicked Priest.
In most EMS system configurations, this level of volume would be a logistical-temporal impossibility for a single ambulance.
Wittgenstein (Tractatus 5.5302) points out that it entails the logical impossibility of a universe containing two identical spheres; Wiggins notes that it implies the logical impossibility of even a single sphere (or any other symmetrical object), since it entails the identity of the two hemispheres (and so on until one reaches a geometrical point).
One galling aspect of selection and the grammar school system is the impossibility of providing a single form of final school-leaving qualification for all pupils that makes sense.
I'd been driven round the bend by the impossibility of having a single conversation with anyone without the subject turning to politics – Trump or Brexit, mainly – and by the mystifying popularity of TV shows and novels with something to say about "the current climate", when clearly what's required is a break from that climate.
