/sci/ - Science & Math

any help with either of these two questions would be appreciated

for the first one, I think the way to go about it is by showing that the supremum of A and the infimum of B are the same thing, but i dont know how to formalize that, showing uniqueness should be easy enough once that is done though

for the second, i can understand intuitively what is going on, that the k sequence is increasing in the naturals, so that the behaviour of the a sequence when "indexed" by k remains the same in the long term, but again, i dont know how to formalize that notion

thanks lads