Cauchy sequence facts for kids
(a) The plot of a Cauchy sequence
shown in blue, as
versus
If the space containing the sequence is complete, the "ultimate destination" of this sequence (that is, the limit) exists.
![(x_n),](/images/math/5/b/1/5b18567a1c4347e544dfbe723148d307.png)
![x_n](/images/math/6/7/b/67b68721103b5a16194f4b3e3ec222db.png)
![n](/images/math/7/b/8/7b8b965ad4bca0e41ab51de7b31363a1.png)
(b) A sequence that is not Cauchy. The elements of the sequence fail to get arbitrarily close to each other as the sequence progresses.
In mathematics, a Cauchy sequence is a sequence where the distance between any two elements of the sequence decreases as the sequence progresses. Cauchy sequences are named after Augustin-Louis Cauchy.
See also
In Spanish: Sucesión de Cauchy para niños
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Cauchy sequence Facts for Kids. Kiddle Encyclopedia.