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e

The symbol e is used almost exclusively to represent the Euler number (aka Euler constant), who value is approximately 2.71828. It may be defined as the limit

\[\lim_{n\rightarrow\infty} \left( 1+ \frac{1}{n}\right) \]

or as the series

\[\sum_{n=0}^{\infty} \frac{1}{n!} = 1 + \frac{1}{2} + \frac{1}{6}+\frac{1}{24}+\cdots\]

Both the logarithm with base e (the so-called natural logarithm) and the exponential function with base e (i.e., the function \(f(x)=e^x\)) are of central importance in many fields of pure and applied mathematics.

Citation Info

  • [MLA] “e.” Platonic Realms Interactive Mathematics Encyclopedia. Platonic Realms, 27 Mar 2013. Web. 27 Mar 2013. <http://platonicrealms.com/>
  • [APA] e (27 Mar 2013). Retrieved 27 Mar 2013 from the Platonic Realms Interactive Mathematics Encyclopedia: http://platonicrealms.com/encyclopedia/e/

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