Page "Limit superior and limit inferior" Paragraph 14

Limits inferior / superior are related to big-O notation in that they bound a sequence only " in the limit "; the sequence may exceed the bound.

However, with big-O notation the sequence can only exceed the bound in a finite prefix of the sequence, whereas the limit superior of a sequence like e < sup >- n </ sup > may actually be less than all elements of the sequence.

The only promise made is that some tail of the sequence can be bounded by the limit superior ( inferior ) plus ( minus ) an arbitrarily small positive constant.