Let the convergence limit of sequence {xn} not be unique.

Lim xn = a, lim xn = b, and e is any positive number.

A and b are not equal.

That is, there is a positive integer N 1, when n >: | xn-a | < E rises constantly.

There is a positive integer N2 when n >: | xn-b |

According to the hypothesis, |a-b|=t

There is an e that satisfies 0.

And when n > Max(N 1, N2),

| a-b | = |(xn-b)-(xn-a)| & lt； = | xn-b |+| xn-a | & lt； =E+E=2E

T< is, t < =2E

It contradicts the hypothesis, so it doesn't hold water.

Prove theorem.

The theorem you ask should be like this. If not, ask again.