# Prove the following. If the sets A and B are bounded above and A ⊆ B, then sup(A) ≤ sup(B)?

• Prove the following. If the sets A and B are bounded above and A ⊆ B, then sup(A) ≤ sup(B)?

sup B is the largest b in B. For all b in B b ≤ sup B A is a subset of B all a in A are also in B all a ≤ sup B sup A is the largest a in A sup A ...
Positive: 38 %
Bounded Sets De nition. We say ... For each of the following sets, decide whether it is bounded, ... numbers satisfying the two conditions above, then b = b0.
Positive: 35 %

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bounded above if there exists ... Exercise 4 For each of the following sets of real ... Give examples of unequal sets for which sup A = sup B and ...
Positive: 38 %
Ris bounded on a non-empty set D then the following ... gare bounded above on a non-empty set S then sup ... bounded above. (b)Prove that ...
Positive: 33 %
Midterm Exam solution ... T F If Aand Bare two bounded sets of real numbers, then sup(A S B) = maxfsupA;supBg. ... (b) Prove (x n) ...