## 3.2. Cauchy Sequences

### Definition 3.2.1: Cauchy Sequence

Let be a sequence
of real (or complex) numbers. We say that the sequence satisfies the

**Cauchy criterion**(or simply is**Cauchy**) if for each*> 0*there is an integer*N > 0*such that if*j, k > N*then| a_{j}- a_{k}| <