Fear of needles to the phobic imagining the procedure being performed on themselves. Recent neuroscience research shows that feeling a pin prick sensation and watching someone else's hand get pricked by a pin activate the same part of the brain. Fear of needles, especially in its more severe forms, is often comorbid with other phobias and psychological ailments; for example, iatrophobia, or an irrational fear of doctors, is often seen in needle phobic patients. A needle phobic patient does not need to physically be in a doctor's office to experience panic attacks or anxiety brought on by needle phobia. There are many triggers
Irrational number A stronger result is the following: Every rational number in the interval formula_23 can be written either as "a" for some irrational number "a" or as "n" for some natural number "n". Similarly, every positive rational number can be written either as formula_24 for some irrational number "a" or as formula_25 for some natural number "n". It is not known if formula_26 (or formula_27) is irrational. In fact, there is no pair of non-zero integers formula_28 for which it is known whether formula_29 is irrational. Moreover, it is not known whether or not the set formula_30 is algebraically independent over