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Problem 77: (Creating Examples Of Bounded Functions)

In each part below, you are asked to state an example. State the example and make sure you justify your claim.

  1. Give an example of a set that is bounded below but not bounded above.
  2. Give an example of a set that is bounded, has a maximum, but does not have a minimum.
  3. Give an example of a noninjective function $f:\mathbb{N}\to \mathbb{R}$ so that $f(\mathbb{N})$ is bounded. Remember, to justify your solution, you'll need to provide upper an lower bounds for $f(\mathbb{N})$.
  4. Give an example of an injective function $f:\mathbb{N}\to \mathbb{R}$ so that $f(\mathbb{N})$ is bounded.

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