Question: Problem 1 (25 marks) Let w E R Q such that w > 0 i.e. @ is a positive irrational number. Define A =

$Problem 1 (25 marks) Let w E R \\ Q such$

Problem 1 (25 marks) Let w E R \\ Q such that w > 0 i.e. @ is a positive irrational number. Define A = {m + nw ER| m + nw > 0 and m, ne Z} (a) Prove that if x, y E A and x > y, then x - y e A. (4 marks) (b) Prove that infA exists and infA 2 0

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1. Identify your reference point when making a decision based on an element of risk.

3. If there are reasonable alternatives, think about your decisions based on the different reference points and see if there are any contradictions in the decisions.

4. It is only at this point that you can give the problem your full attention in relation to the various ways you have framed the problem.