Difference between revisions of "E-number"
From Encyclopedia of Mathematics
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| − | The limit of the expression | + | {{TEX|done}} |
| + | The limit of the expression $(1+1/n)^n$ as $n$ tends to infinity: | ||
| − | + | $$e=\lim_{n\to\infty}\left(1+\frac1n\right)^n=2.718281828459045\ldots;$$ | |
| − | it is the base for the natural logarithm. | + | it is the base for the natural logarithm. $e$ is a transcendental number, which was proved by C. Hermite in 1873 for the first time. Sometimes $e$ is called the Napier number for no very good reason. |
Revision as of 21:59, 11 April 2014
The limit of the expression $(1+1/n)^n$ as $n$ tends to infinity:
$$e=\lim_{n\to\infty}\left(1+\frac1n\right)^n=2.718281828459045\ldots;$$
it is the base for the natural logarithm. $e$ is a transcendental number, which was proved by C. Hermite in 1873 for the first time. Sometimes $e$ is called the Napier number for no very good reason.
Comments
See also Exponential function; Exponential function, real; Logarithm of a number; Logarithmic function; Transcendental number.
How to Cite This Entry:
E-number. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=E-number&oldid=17180
E-number. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=E-number&oldid=17180
This article was adapted from an original article by S.A. Stepanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article