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(→As an infinite series: minor simplification: 3  \sum_{k=2}^\infty \frac{1}{k! (k1) k}) 
(→As the limit of a sequence: Added factorial/derangement definition.) 

:<math>e= \lim_{n \to \infty}\left (1+ \frac{1}{n} \right )^n.</math>
The ratio of the [[factorial]] <math>n!</math>, that counts all [[permutationpermutations]] of an orderet set S with [[cardinality]] <math>n</math>, and the [[derangement]] function <math>!n</math>, which counts the amount of permutations where no element appears in its original position, tends to <math>e</math> as <math>n</math> grows.
:<math>e= \lim_{n \to \infty} \frac{n!}{!n}.</math>
== In trigonometry ==

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