The following equation should be true: $O(n\log(n))=O(n^{1.1} )$
Based on the following article, one should see the equation as the left part being an element of the right part. What are the rules for equals signs with big-O and little-o?
Given that the equation is true, $n\log(n)$ should grow at most as fast as $n^{1.1}$. However, $\lim_{n \to \infty} \frac{n\log(n)}{n^{1.1}}=\lim_{n \to \infty} \frac{\log(n)}{n^{0.1}} \rightarrow \infty$. This does not correspond with the statement.
What mistake am I making?
What is true, really, is this: $$O(n\log n)=o\bigl(n^{1.1}\bigr).$$