A question about the proof that the convergence of sequence of higher numbers must be bounded This theorem is proved in page 40 of the fourth edition of Tongji, because the sequence {xn} converges, let limxn = a, according to the definition of sequence limit, there exists positive integer n for ε = 1, such that for all xn when n > N, when the inequality | xn-a | n, | xn | = | (xn-a) + a | ≤ | xn-a | + | a|

A question about the proof that the convergence of sequence of higher numbers must be bounded This theorem is proved in page 40 of the fourth edition of Tongji, because the sequence {xn} converges, let limxn = a, according to the definition of sequence limit, there exists positive integer n for ε = 1, such that for all xn when n > N, when the inequality | xn-a | n, | xn | = | (xn-a) + a | ≤ | xn-a | + | a|

Please note that when n > N, | xn | = | (xn-a) + a | ≤| xn-a | + | a | n, and N ≤ n, | xn | ≤ 1 + | a |, may not be true