Cauchy convergence test | Cauchy's criterion (English)
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Definition (undergraduate level)
A sequence converges if and only if it is a Cauchy sequence,
i.e. for any ε > 0, there is a natural number N such that |xn − xm| < ε for all m,n > N.
i.e. for any ε > 0, there is a natural number N such that |xn − xm| < ε for all m,n > N.
Relations
- broader:
- (en) Test
- (en) Theorem
- references:
- (en) Cauchy sequence
- (en) Converge
- referenced:
- (en) Cauchy
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