CANNOT HAPPEN›If an action or event is impossible, it cannot happen or be done: an impossible taskHe finds walking almost impossible.[+ to do sth]It was impossible to sleep because of the noise.
DIFFICULT›very difficult to deal with: You just can't reason with her, she's absolutely impossible.You're putting me in an impossible position.
impossibility
/ɪmˌpɒsəˈbɪləti/noun[C, U]›when something is impossible: [usually singular]I can't do it - it's a physical impossibility.