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Cauchy Sequence

A sequence a_1, a_2, ... such that the metric d(a_m,a_n) satisfies

lim_(min(m,n)->infty)d(a_m,a_n)=0.

Cauchy sequences in the rationals do not necessarily converge, but they do converge in the reals.

Real numbers can be defined using either Dedekind cuts or Cauchy sequences.

See also

Dedekind Cut

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Cite this as:

Weisstein, Eric W. "Cauchy Sequence." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CauchySequence.html

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