Relation Between Minimums And Infimums

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Problem 29: (Relation Between Minimums And Infimums)

Suppose $S$ is a set of real numbers.

• If $m$ is the minimum of $S$, must $m$ be the infimum of $S$? Prove your claim.
• If $m$ is the infimum of $S$, must $m$ be the minimum of $S$? Prove your claim.

(Similar facts hold true for the maximum and supremum of a set.)

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