Emetophobia activities so they avoid any situations with alcohol or dining out in restaurants. Emetophobics may also limit exposure to children for fear of germs. Females who suffer from this disorder delayed pregnancy or avoided it altogether because of the fear of morning sickness. People who have a fear of vomiting may avoid travel because of the worry about motion sickness or others experiencing it around them. They may also fear roller coasters for the same reason. Dr. Lipsitz "et al".'s findings also showed that those afflicted with emetophobia often have difficulties comfortably leading a normal life. Many find that they
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