Fear of fish footballer Paolo Di Canio describes finding that his then team-mate, Peter Grant suffered from ichthyophobia. During a practical joke, Di Canio describes Grant's fearful reaction after finding a salmon head in his bed. Grant told "The Independent" that item in his bed was in fact a "shark's head" and "to say I got a fright when I put my feet between the sheets is an understatement." The term "ichthyophobia" comes from the Greek ἰχθῦς - "ichthus", meaning "fish" and φόβος - "phobos", "fear". "Galeophobia" comes from the Greek γαλεός - "galeos", "small shark". Fear of fish Fear of fish or
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