Is it not equivalent to "lim" rather than "lim sup"? Can you explain this part? I thought the definition of "lim" is *exactly* the eps/delta construction for big O. So I don't understand why you need to use lim sup. Also, are you using [this](http://en.wikipedia.org/wiki/Limit_superior_and_limit_inferior#Functions_from_metric_spaces_to_metric_spaces) definition of lim sup?

Not a big deal to merging this PR, it's just a one word change.