(a) Let A and B be non-empty, bounded subsets of R. Define the set {(x+y)/2: x...

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(a) Let A and B be non-empty, bounded subsets of R. Define the set {(x+y)/2: x EA and y € B} . Show that T = sup(T) = sup(A) + sup(B) 2 [8] (b) Use any of the convergence tests to show that both of the following series diverge: Σ and 1 亦 j=1 (a) Let A and B be non-empty, bounded subsets of R. Define the set {(x+y)/2: x EA and y € B} . Show that T = sup(T) = sup(A) + sup(B) 2 [8] (b) Use any of the convergence tests to show that both of the following series diverge: Σ and 1 亦 j=1

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a Let C xy2 x A and y B To show that T supC supA supB we will prove the following two statements sup... View the full answer