EDIT: Apparently I translated the terminology wrong, but partial limit means limit of a subsequence.
If $a_{n}$ has 'a' partial limits and $b_{n}$ has 'b', can $a_{n}+b_{n}$ have more than $ab$ partial limits? ('infinity' also counting as a limit)
This is a homework question. I'm thinking the statement is false, but I have no idea where to begin! Could someone give me a hint?
Thanks!