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Cauchy sequence (English)

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Definition (undergraduate level)

A sequence x_n with the property that for any ε > 0, there is a natural number N such that |x_n − x_m | < ε for all m,n > N.

Definition (undergraduate level)

A sequence (x_n) with the property that

∀ε > 0 , ∃N ∈ N : ∀m,n ≥ N , d(x_m,x_n) < ε,

where d is the distance function on the metric space in which the sequence lies.

Relations

broader:: (en) Sequence
referenced:: (en) Cauchy; (en) Cauchy convergence test; (en) Complete

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