The problem involves proving a relationship between the limit superior of the product of two bounded positive sequences and the limit superiors of the individual sequences. The original poster seeks to establish that limsup(anbn) is less than or equal to limsup(an) times limsup(bn) and to provide an example illustrating that equality does not hold in general.
The discussion is ongoing, with participants exploring the relationship between the sequences and their limit superiors. Guidance has been offered to clarify the initial steps needed to approach the proof, but no consensus has been reached on the method or final outcome.
There is an emphasis on the requirement for participants to demonstrate their own attempts at solving the problem to maintain the thread's validity. The original poster has provided a specific example of sequences, but further details are not yet discussed.
