e, in mathematics

e, in mathematics, irrational number occurring widely in mathematics and science, approximately equal to the value 2.71828; it is the base of natural, or Naperian, logarithms. The number e is defined as the limit of the expression (1+1/n)n as n becomes infinitely large, or CE5 In 1873 the French mathematician C. Hermite proved that e was transcendental, i.e., not a root of any algebraic equation; this proof constituted a great contribution to the growth of mathematics. The number e is also known as Euler's number, for Leonhard Euler, who discovered the famous formula eiπ=−1, where i= (1), thus expressing the relationship between the numbers e, i, and π. The exponential function ex, often written exp(x), occurs in various applications ranging from statistics to nuclear physics.

See study by E. Maor (1994).

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