Then, if the series is not normalized, consider the first nonzero that is not an integer in the interval The second above lemma allows writing it one gets n equivalent series by replacing with and adding to Iterating this process, possibly infinitely many times, provides eventually the desired normalized -adic series.
Then, if the series is not normalized, consider the first nonzero that is not an integer in the interval The second above lemma allows writing it one gets n equivalent series by replacing with and adding to Iterating this process, possibly infinitely many times, provides eventually the desired normalized -adic series