On Tue, Nov 19, 2013 at 04:32:52PM -0800, Ondřej Čertík wrote:
>  >      The formal definition for the order of a function `g(x)` about a point `a`
>  >      is such that `g(x) = O(f(x))` as `x \rightarrow a` if and only if for any
>  >      `\delta > 0` there exists a `M > 0` such that `|g(x)| \leq M|f(x)|` for
>  >      `|x-a| < \delta`. This is equivalent to `\lim_{x \rightarrow a}
>  > -    |g(x)/f(x)| < \infty`.
>  > +    \sup |g(x)/f(x)| < \infty`.
> 
>    Is it not equivalent to "lim" rather than "lim sup"?

No, the previous assertion was wrong.

>    So I don't understand why you need to use lim sup.

The reason, that the first definition is comming from
http://en.wikipedia.org/wiki/Big_O_notation#Formal_definition
And it's not equivalent to "lim", but "lim sup:

>    Also, are you using [1]this definition of lim sup?

http://en.wikipedia.org/wiki/Limit_superior

>    Not a big deal to merging this PR, it's just a one word change.

But it's important too.