I am studying Algorithms on my own from the CLRS book, i.e. Introduction to Algorithms by Cormen etc. I need help to understand some math in the book.
The book says that the functions $$ n $$ and $$ n^{1+\sin (n)} $$ cannot be compared using asymptotic notation, since the value of the exponent in the latter function oscillates between 0 and 2, taking on all values in between.
Why can the two functions not be compared using asymptotic notation ? Can someone please explain in more detail, preferably with a diagram ?
Thank you.
For large $n$ you cannot say that one graph dominates the other.
Click for a closer look. https://www.desmos.com/calculator/uhvcmgxyg1