infimum of set of real numbers bounded below

Task number: 2829

Let \(M\) be a sequence of real numbers that is bounded below. Show that it has a (real) infimum. (You may use the existence of a supremum for a set of numbers that is bounded above.)

  • Resolution

    The set \(-M := \{-x \colon x \in M\}\) is bounded above, so it has a supremum \(s\). Then \(-s\) is an infimum of the set \(M\).

Difficulty level: Easy task (using definitions and simple reasoning)
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