The Hare's Criterion

Hare's Criterion is a mathematical test used to determine if a sequence of numbers converges to a limit. It states that if, for every small positive number (called epsilon), there is a certain point in the sequence beyond which all subsequent terms stay within that epsilon distance from a specific value (the limit), then the sequence converges to that value. In simple terms, once you reach a certain stage, all the remaining terms stay very close to the target value, confirming the sequence approaches and approaches that limit but never diverges away.