Difference between revisions of "E-number"
From Encyclopedia of Mathematics
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(See "E: the story of a number" by Maor) |
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$$e=\lim_{n\to\infty}\left(1+\frac1n\right)^n=2.718281828459045\ldots;$$ | $$e=\lim_{n\to\infty}\left(1+\frac1n\right)^n=2.718281828459045\ldots;$$ | ||
| − | 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. | + | 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. |
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====Comments==== | ====Comments==== | ||
See also [[Exponential function|Exponential function]]; [[Exponential function, real|Exponential function, real]]; [[Logarithm of a number|Logarithm of a number]]; [[Logarithmic function|Logarithmic function]]; [[Transcendental number|Transcendental number]]. | See also [[Exponential function|Exponential function]]; [[Exponential function, real|Exponential function, real]]; [[Logarithm of a number|Logarithm of a number]]; [[Logarithmic function|Logarithmic function]]; [[Transcendental number|Transcendental number]]. | ||
Revision as of 19:55, 14 October 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.
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=31585
E-number. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=E-number&oldid=31585
This article was adapted from an original article by S.A. Stepanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article