What does the definition of sequence limit mean?

Sequence limit definition Let {xn} be a sequence. If there is a constant a, for any given positive number ε (no matter how small it is), there will always be a positive integer N, such that when n>N? When, the inequalities

are all established, then the constant a is said to be the limit of the sequence {xn}, or the sequence {xn} converges to a, which is recorded as

a geometric explanation

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From the first volume of Tongji University