1. An example of a discontinuous function on an interval [a,b] that does not assume every value between f(a) and f(b).(adsbygoogle = window.adsbygoogle || []).push({});

[edit] My answer to this: Piecewise function f(x)= 1/x, for x greater than and equal to -4 but less than zero (0). And f(x)=1/x for x greater than zero but less than and equal to 4. This makes the function discontinuous, on the interval [-4,4]. Now, I let c=0. There does not exist a value x in (-4,4) such that f(x)=c. Correct?

2. Find a nested sequence of non-compact sets whose intersection is empty.

3. An example of an unbounded infinite set that has no accumulation point.

For this one, I know that 1/n, for n=1,2,3,... has ONLY zero as an accumulation point, so can I maybe do something like {1/n}U{0} so that there is no longer an accumulation point? I'm pretty suck on this one.

[edit] (I figured out #4 and #5 now )

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