Cauchy Sequence

A Cauchy sequence is a series of numbers where, as you progress through the sequence, the values become increasingly close to each other. Essentially, for any small distance you choose, no matter how tiny, there comes a point in the sequence where all subsequent numbers differ from each other by less than that distance. This concept helps in understanding convergence; if a sequence is Cauchy, it suggests that the numbers will cluster around a specific value, even if that value isn't explicitly defined within the sequence itself. This is important in mathematics for defining limits and continuity.