Spectrophobia distorted in strange ways or their reflection may frighten them. Some people may also fear being pulled into the mirror by some preternatural force. Spectrophobia Spectrophobia (from Latin: "spectrum", n. specio, an appearance, form, image of a thing; an apparition, spectre) or catoptrophobia (from Greek κάτοπτρον "kátoptron", "mirror") is a kind of specific phobia involving a morbid fear of mirrors, sometimes related to the fear of ghosts or the undead. This phobia is distinct from eisoptrophobia, which is the fear of one's own reflection. Generally, an individual that deals with spectrophobia has been traumatized in an event where they believe
Proof that e is irrational 1. For all terms with we have the upper estimate This inequality is strict for every "n" ≥ "b" + 2. Changing the index of summation to "k" = "n" – "b" and using the formula for the infinite geometric series, we obtain Since there is no integer strictly between 0 and 1, we have reached a contradiction, and so "e" must be irrational. Q.E.D. Another proof can be obtained from the previous one by noting that and this inequality is equivalent to the assertion that "bx" < 1. This is impossible, of course, since "b" and "x" are natural