impossibility
n.something that cannot happen or be done because it is not possible. You use this word to describe a situation that has no solution.
n.the state or fact of being unable to occur, exist, or be achieved. Often used to describe a logical or physical contradiction.
“Traveling faster than the speed of light is a physical impossibility.”
“The team realized that finishing the entire project by tomorrow morning was a mathematical impossibility.”
“The philosopher argued that the coexistence of these two opposing laws was a logical impossibility within a single legal framework.”
Often follows the indefinite article 'an' when referring to a specific impossible task or situation.
“FACUA has provided the Consumer Affairs Department with evidence of calls made demonstrating the impossibility of speaking to a person through the telephone lines available to users.”
“Playing a high-energy pressing game in four or five competitions will quickly become an impossibility.”
From Middle French impossibilité, from Latin impossibilitās. By surface analysis, im- + possibility and impossible + -ity.
Etymology adapted from Wiktionary, available under CC BY-SA 4.0.