Cauchy Sequence

analysis

Definition

Cauchy Sequence

A real sequence is called cauchy sequence, named after Augustin-Louis Cauchy, if for all $\epsilon >0$ there exists an $N(\epsilon )$, such that:

$$\forall n,m>N(\epsilon ):|a_n-a_m|<\epsilon$$

Cauchy sequences are convergent and all convergent sequences are Cauchy sequences.