Prove: diverges

For every L there exists an epsilon greater than zero, for every N greater than 0, n>0.

So,

Pf: Let be given. Set and let be given. There exists s.t. . Then, if , we would have . But then if we would have . So, . But then would be in different intervals. Thus the sequence diverges as desired.

Is this the correct way to go about this?

Thx!