So I'm doing some exercise on sequences, and one of the question is giving a hard time. It requires me to give an example of 2 bounded non-negative sequences $x_n$ and $y_n$ such that
lim sup ($x_ny_n$) < lim sup($x_n$) . lim sup($y_n$)
All the examples I thought of ended up in an equality instead of the strictly lesser than inequality. Does anyone know any simple examples for this ?