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www.jeremykun.com | ||
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algorithmsoup.wordpress.com
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| | | | | The ``probabilistic method'' is the art of applying probabilistic thinking to non-probabilistic problems. Applications of the probabilistic method often feel like magic. Here is my favorite example: Theorem (Erdös, 1965). Call a set $latex {X}&fg=000000$ sum-free if for all $latex {a, b \in X}&fg=000000$, we have $latex {a + b \not\in X}&fg=000000$. For any finite... | |
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xorshammer.com
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| | | | | There are a number of applications of logic to ordinary mathematics, with the most coming from (I believe) model theory. One of the easiest and most striking that I know is called Ax's Theorem. Ax's Theorem: For all polynomial functions $latex f\colon \mathbb{C}^n\to \mathbb{C}^n$, if $latex f$ is injective, then $latex f$ is surjective. Very... | |
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thehousecarpenter.wordpress.com
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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... | |
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cardinalguzman.wordpress.com
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| | | Encyclopedia Miscellaneous - 'quality' blogging since August 2011 | ||
