Caret confused with other chevron-shaped characters, such as or , which may occasionally be called carets, too. The caret was originally and continues to be used in handwritten form as a proofreading mark to indicate where a punctuation mark, word, or phrase should be inserted into a document. The term comes from the Latin , "it lacks", from , "to lack; to be separated from; to be free from". The caret symbol is written below the line of text for a line-level punctuation mark, such as a comma, or above the line as an inverted caret (cf. ) for a higher
Proof that e is irrational Proof that e is irrational The number "e" was introduced by Jacob Bernoulli in 1683. More than half a century later, Euler, who had been a student of Jacob's younger brother Johann, proved that "e" is irrational; that is, that it cannot be expressed as the quotient of two integers. Euler wrote the first proof of the fact that "e" is irrational in 1737 (but the text was only published seven years later). He computed the representation of "e" as a simple continued fraction, which is Since this continued fraction is infinite and every rational number has a terminating continued