Cauchy sequence
(a) The plot of a Cauchy sequence <math>(x_n),</math> shown in blue, as <math>x_n</math> versus <math>n</math> 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.
