Halmos's set theory If $E$ is a non-empty set of natural numbers, exists some $k$ in $E$ such that $k \leqq m$ for all $m\in E$. Prove by intersection

score 58 · Answer 14 · 2022-02-03 21:14:41

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How can I proove only one of these three holds? $m>n, m=n, m<n$.

Published on 03 Feb 2022 - 21:14

score 75 · Answer 15 · 2026-03-29 10:46:38

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Are there any arithmetic statements where there does not exist a proof proving the statement?

Published on 29 Mar 2026 - 10:46

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Halmos's set theory If $E$ is a non-empty set of natural numbers, exists some $k$ in $E$ such that $k \leqq m$ for all $m\in E$. Prove by intersection

How can I proove only one of these three holds? $m>n, m=n, m<n$.

Are there any arithmetic statements where there does not exist a proof proving the statement?

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