Logarithmic number system: Difference between revisions
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en>Qwertyus →Applications: Logarithms are commonly used in Viterbi (and any other algorithm that works with probabilities), but not necessarily LNS |
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{{Portal:Mathematics/Feature article|img=Exp derivative at 0.svg|img-cap= ''e'' is the unique number such that the slope of ''y''=''e<sup>x</sup>'' (blue curve) is exactly 1 when ''x''=0 (illustrated by the red [[Point_of_tangency|tangent line]]). For comparison, the curves ''y''=2<sup>x</sup> (dotted curve) and ''y''=4<sup>x</sup> (dashed curve) are shown.|img-cred=[[User:Dicklyon|Dick Lyon]]|more=e (mathematical constant)|desc=[[e (mathematical constant)|The mathematical constant '''''e''''']] is occasionally called '''Euler's number''' after the [[Switzerland|Swiss]] [[mathematician]] [[Leonhard Euler]], or '''Napier's constant''' in honor of the [[Scotland|Scottish]] mathematician [[John Napier]] who introduced [[logarithm]]s. It is one of the most important numbers in mathematics, alongside the additive and multiplicative identities [[0 (number)|0]] and [[1 (number)|1]], the [[imaginary unit]] ''i'', and [[pi|π]], the circumference to diameter ratio for any circle. It has a number of equivalent definitions. One is given in the caption of the image to the right, and three more are: | |||
# The sum of the [[infinite series]] | |||
#:<math>\begin{align} e & = \sum_{n = 0}^\infty \frac{1}{n!} \\ | |||
& = \frac{1}{0!} + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \cdots \\ \end{align}</math> | |||
#:where ''n''! is the [[factorial]] of ''n''. | |||
#: | |||
# The [[global maximum]] of the function | |||
#:<math> f(x) = x^{1 \over x}. </math> | |||
#: | |||
# The [[limit (mathematics)|limit]]: | |||
#:<math>e = \lim_{n\to\infty} \left( 1 + \frac{1}{n} \right)^n</math> | |||
#:: | |||
The number ''e'' is also the base of the [[natural logarithm]]. Since ''e'' is [[transcendental number|transcendental]], and therefore [[irrational number|irrational]], its value can not be given exactly. The numerical value of ''e'' truncated to 20 [[decimal|decimal places]] is 2.71828 18284 59045 23536. |class={{{class}}}}} | |||
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Revision as of 15:54, 17 July 2013
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