First of all, I apologize if this question is too elementary or pedantic. It is usually said that every non-empty set of natural numbers has a least element. However, books usually don't mention if the least element is unique. So, what is the proof that the least element in a non-empty set of natural numbers is unique?
2026-04-01 09:50:41.1775037041
Does every non-empty set of natural numbers have a unique least element?
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Ordering on the natural numbers is anti-symmetric, i.e. if $x\leq y$ and $y\leq x$ then $x=y$