Question

1. Show there exists a nested sequence of closed intervals ([an, bn]) such that a) [an+1,...

1. Show there exists a nested sequence of closed intervals ([an, bn]) such that

a) [an+1, bn+1] contains [an, bn] contains [0,1] for n=1, 2...

b) f(n) is not an element of [an, bn]

2. Use the Bounded Monotone Convergence Theorem to show (an) and (bn) converge. Let (an) go to A, (bn) go to B. Then [an, bn] got to [A, B].

3. Prove A is an element of [an, bn] for every n = 1, 2, 3, ... Conclude that A is not an element of f(N).

4. Finish the proof that f is not onto.

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