Your definition seems to be correct.
Now, you can try for a contradiction/contrapositive by constructing an increasing sequence which diverges to infinity but does not.
Suppose and . Prove that for every increasing sequence in , if , then .
I'm trying to prove [<==] when by contradiction. But not sure about the definition:
means that , there is such that Is this the correct definition?
So if , then there exists such that there exists such that Right?