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 can never be expressed as a quotient of integers "m"/"n" with "n" ≠ 0. Cases such as log 2 can be treated similarly. Almost all irrational numbers are transcendental and all real transcendental numbers are irrational (there are also complex transcendental numbers): the article on transcendental numbers lists several examples. So "e" and π are irrational for all nonzero rational "r", and, e.g., "e" is irrational, too. Irrational numbers can also be found within the countable set of real algebraic numbers (essentially defined as the real roots of polynomials with integer coefficients), i.e., as real solutions of polynomial equations where