This article defines the limit of a sequence of numbers. Note that for any given e, if there is N(N is arbitrary, but it must exist) and there is always | xn-a | < E, a is called the limit of the sequence.

A is not given at will, e is given at will.

It can be understood that the limit A of a sequence is determined by its existence, but how to prove it is a limit depends on this definition.