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 \(M\).
