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| | francisbach.com
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| | algorithmsoup.wordpress.com
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| | This is part of a new sequence of posts titled, My favorite example of: $latex {x}&fg=000000$, for different values of $latex {x}&fg=000000$. Today, $latex {x}&fg=000000$ is the pigeonhole principle. The Erdös-Szekeres Theorem: Consider any sequence of $latex {n}&fg=000000$ distinct numbers. There must exist a subsequence $latex {S}&fg=000000$ of $latex {\sqrt{n}}&fg=000000$ numbers such that $latex {S}&fg=000000$...
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| NB: I've opted to just get straight to the point with this post rather than attempting to introduce the subject first, so it may be of little interest to readers who aren't already interested in proving the completeness theorem for propositional logic. A PDF version of this document is available here. The key thing I...