Emetophobia up. Some may have both. Some may have anxiety which makes them feel like they will throw up when they actually might not. People with emetophobia usually suffer from anxiety; they often may scream or cry when someone or something has been sick. The root word for emetophobia is "emesis", from the Greek word "emein", which means "an act or instance of vomiting", with "-phobia" meaning "an exaggerated usually inexplicable fear of a particular object, class of objects, or situation." People with emetophobia frequently report a vomit related traumatic event, such as a long bout of stomach flu, accidentally vomiting
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