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.
shown in blue, as versus If the space containing the sequence is complete, the "ultimate destination" of this sequence (that is, the limit) exists.
(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.