## 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 \(M\).