Emetophobia vomiting, thus inducing a phobia." In an internet survey conducted by Dr. Joshua D. Lipsitz "et al." given to emetophobic people, respondents gave many different reasons as to why they became emetophobic. Among some of the causes listed were several severe bouts of vomiting as children and being firsthand witnesses to many severe vomiting in others due to illness, pregnancy or alcoholism. There are two assessment tools used to diagnose emetophobia: the Specific Phobia of Vomiting inventory and the Emetophobia Questionnaire. They are self-report questionnaires that focus on a different range of symptoms. There have been a limited number of
Proof that π is irrational sine and cosine function are given by sin' = cos and cos' = −sin. Hence the product rule implies By the fundamental theorem of calculus Since and (here we use the above-mentioned characterization of as a zero of the sine function), Claim 2 follows. Conclusion: Since and for (because is the "smallest" positive zero of the sine function), Claims 1 and 2 show that is a "positive" integer. Since and for , we have, by the original definition of "f", which is smaller than 1 for large "n", hence for these "n", by Claim 2. This is impossible for the