Let W be a nonempty subset of R that is bounded above, and define the set B as follows B= {N ER:N is an upper bound of W } %3| Prove supW = inf B %3D

Q: Let A be a non-empty subset of R which is bounded below and let B be the subset of R defined by B =…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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Q: below. If y = inf S, show that, for each delta> 0, there is s ∈ S such that y ≤ s < y + delta .

A: Adding equation 1 and 2 we get our result.

Q: (b) Consider the set Prove that inf A = 0. A = { n m² : n,m € Z¹, m≤n}.

A: Our objective is given below:

Q: Let A be a non-empty subset ofR which is bounded below and let B be the subset of R defined by B =…

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A: Follow the steps.

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Q: Show that if A and B are bounded subsets of IR, then inf(A U B) = min{inf A.inf B}. %3D

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