I have a simple question:

It is conjectured that the shortest path of all pairs (APSP) does not have $ O (n ^ {3- delta)} $time algorithm for any $ delta> 0 $ by SETH.

also

there is a result that says that APSP can be resolved in time $ frac {n ^ 3} {2 ^ { Omega ( sqrt { log n})}} $ by Ryan Williams.

But, this improvement does not refute the guesswork.

So what I did is this: I compare between $ lim_ {n -> infty} frac {( frac {n ^ 3} {2 ^ { sqrt { log n}}})} {n ^ {3- delta}} = 0 $ So, $ frac {n ^ 3} {2 ^ { Omega ( sqrt { log n})}} $ is better than the other, so why doesn't that mean we refute the conjecture?

When I have this function: $ frac {n ^ 3} {2 ^ { Omega ( sqrt { log n})}} $I did not know how to compare it with others, since Big Omega is only a part, how to compare in general with other functions when you have this?

Thanks in advance!