Emetophobia these fears can become so ingrained that the person who has them can begin to suffer from anorexia nervosa. Emetophobia Emetophobia is a phobia that causes overwhelming, intense anxiety pertaining to vomiting. This specific phobia can also include subcategories of what causes the anxiety, including a fear of vomiting in public, a fear of seeing vomit, a fear of watching the action of vomiting or fear of being nauseated. It is common for emetophobics to be underweight, or even anorexic, due to strict diets and restrictions they make for themselves. The thought of someone possibly vomiting can cause the phobic
Irrational number if complex number exponentiation is used). An example that provides a simple constructive proof is The base of the left side is irrational and the right side is rational, so one must prove that the exponent on the left side, formula_17, is irrational. This is so because, by the formula relating logarithms with different bases, which we can assume, for the sake of establishing a contradiction, equals a ratio "m/n" of positive integers. Then formula_19 hence formula_20 hence formula_21 hence formula_22, which is a contradictory pair of prime factorizations and hence violates the fundamental theorem of arithmetic (unique prime factorization).