those three approximations, all of the remaining approximations are within the error range . The same approximation property holds for every positive error .

More precisely, a sequence of real numbers is said to be convergent if there exists an such that for each positive real number , there exists a positive integer (depending on ) such that every term with is within distance of . The number is unique, when it exists. It is called the limit of the sequence , and this is written

The definition of the limit of a sequence

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