i need to prove or disprove the following:
thanks in advanced!
both sets are bounded from above.
I've found the following to be useful:
supremums of larger sets are larger and infimums of larger sets are smaller
Formally, (assuming the sets are bounded):
1. If then
2. If then
Proof of 1 - Let . Let , then and so ; i.e. is an upper bound of . So . The proof for infs is exactly similar.
For your original question, since , , and similarly for B.