Let X be a nonempty set, and let f and g be defined on X and have bounded ranges in
Chapter 2, Problem 7(choose chapter or problem)
Let X be a nonempty set, and let f and g be defined on X and have bounded ranges in JR.Show that sup{f(x) + g(x): x eX} :s sup{f(x) : x eX} + sup{g(x) : x eX} and that inf{f(x) : x e X}+ inf{g(x) : x e X} :s inf{f(x) + g(x) : x eX}. Give examples to show that each of these inequalities can be either equalities or strict inequalities.
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