Namespaces
Variants
Actions

Difference between revisions of "E-number"

From Encyclopedia of Mathematics
Jump to: navigation, search
(Importing text file)
 
(TeX)
Line 1: Line 1:
The limit of the expression <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035010/e0350102.png" /> as <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035010/e0350103.png" /> tends to infinity:
+
{{TEX|done}}
 +
The limit of the expression $(1+1/n)^n$ as $n$ tends to infinity:
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035010/e0350104.png" /></td> </tr></table>
+
$$e=\lim_{n\to\infty}\left(1+\frac1n\right)^n=2.718281828459045\ldots;$$
  
it is the base for the natural logarithm. <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035010/e0350105.png" /> is a transcendental number, which was proved by C. Hermite in 1873 for the first time. Sometimes <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035010/e0350106.png" /> is called the Napier number for no very good reason.
+
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=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