Emetophobia in public or having to witness someone else vomit, as the start of the emetophobia. They may also be afraid of hearing that someone is feeling like vomiting or that someone has vomited, usually in conjunction with the fears of seeing someone vomit or seeing vomit. There is a strong agreement in the scientific community that there is no specific cause of emetophobia. Some emetophobics report a traumatic experience with vomiting, always in childhood. Some suggest that sufferers are victims of childhood abuse – sexual or physical. While this is occasionally true, it seems to be no more prevalent than
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).