Fear of flying persistent fear or anxiety when they consider flying, as well as during flying. They will avoid flying if they can, and the fear, anxiety, and avoidance cause significant distress and impair their ability to function. Take-off, bad weather, and turbulence appear to be the most anxiety provoking aspects of flying. The most extreme manifestations can include panic attacks or vomiting at the mere sight or mention of an aircraft or air travel. Around 60% of people with fear of flying report having some other anxiety disorder. The causes of flight phobia and the mechanisms by which it is maintained were
Irrational number Consider ; if this is rational, then take "a" = "b" = . Otherwise, take "a" to be the irrational number and "b" = . Then "a" = () = = = 2, which is rational. Although the above argument does not decide between the two cases, the Gelfond–Schneider theorem shows that is transcendental, hence irrational. This theorem states that if "a" and "b" are both algebraic numbers, and "a" is not equal to 0 or 1, and "b" is not a rational number, then any value of "a" is a transcendental number (there can be more than one value