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
Thomae's function Then, necessarily, formula_66 and therefore, Likewise, for all irrational formula_68 and thus, if formula_69 then any choice of (sufficiently small) formula_70 gives Therefore, formula_7 is continuous on formula_73 A natural follow-up question one might ask is if there is a function which is continuous on the rational numbers and discontinuous on the irrational numbers. This turns out to be impossible; the set of discontinuities of any function must be an set. If such a function existed, then the irrationals would be an set. The irrationals would then be the countable union of closed sets formula_90, but since the irrationals do