Cauchy Sequences

A Cauchy sequence is a series of numbers where, as you look further along the sequence, the numbers become increasingly close to each other. In simpler terms, no matter how small a distance you choose, you can eventually find terms in the sequence that are all within that distance from each other. This concept helps us understand convergence in mathematics; if a sequence is Cauchy, it means that it approaches a specific value or point as you progress. In complete spaces like real numbers, every Cauchy sequence converges to a limit.