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 then no integral power of it can be an integer, as in lowest terms there must be a prime in the denominator that does not divide into the numerator whatever power each is raised to. Therefore, if an integer is not an exact "k" power of another integer, then that first integer's "k" root is irrational. Perhaps the numbers most easy to prove irrational are certain logarithms. Here is a proof by contradiction that log 3 is irrational. Notice that log 3 ≈ 1.58 > 0. Assume log 3 is rational. For some positive integers "m" and "n", we have