A The so-called limit of an is equal to a, which refers to how close the value of an is to A, that is, given a positive number ε (ε is a constant proximity, which can be arbitrarily small), all items in the sequence that always come from a certain item are closer to A than ε.

Expressed by mathematical symbols: for any positive number ε >; 0, there is N>0, and when n> is n, there is | an-a | < ε.

Note that this n may or may not depend on ε. It doesn't matter how much n equals, as long as there is such a positive number. So the value of n is not unique. For example, all items starting from 10000 satisfy | an-a | < ε, then all items after 1000000 naturally satisfy | an-a |.

Because ε is different, the inequality above is different, and the n obtained is different.