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
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