Cauchy Criterion

The Cauchy criterion is a mathematical concept used to determine whether a sequence of numbers approaches a specific value, known as a limit. In simple terms, it states that if the terms of a sequence can be made arbitrarily close to each other as you go further along, then the sequence converges to a limit. This means for any small distance you choose, there’s a point in the sequence beyond which all terms stay within that distance of each other. If a sequence meets this condition, it behaves predictably and approaches a specific value as you continue along it.