Let S be an ordered set. Let A ⊂ S be a nonempty finite subset. Then A is bounded. Furthermore, inf A exists and is in A and sup A exists and is in A. Hint: Use induction.
How do I use induction to prove that the infinum and supremum exist?
2026-04-04 10:17:29.1775297849
A finite subset of an ordered set contains an $\inf$ and $\sup$
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