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nickdrozd.github.io
| | neilmadden.blog
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| | I saw another article on Gödel's incompleteness theorems linked from Reddit today. It's a topic I've wanted to write about for some time. Although many articles do a decent job in giving an idea of what the big deal is (and this one is pretty good), they can sometimes give a misleading impression of what...
| | 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...
| | xorshammer.com
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| | Let $latex \mathrm{PA}$ be Peano Arithmetic. Gödel's Second Incompleteness Theorem says that no consistent theory $latex T$ extending $latex \mathrm{PA}$ can prove its own consistency. (I'll write $latex \mathrm{Con}(T)$ for the statement asserting $latex T$'s consistency; more on this later.) In particular, $latex \mathrm{PA} + \mathrm{Con}(\mathrm{PA})$ is stronger than $latex \mathrm{PA}$. But certainly, given that...
| | blog.samibadawi.com
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| [AI summary] A developer reflects on the trade-offs between static and dynamic typing systems, discussing their experiences with functional languages like Haskell, Scala, and Clojure in contexts ranging from production stability to NLP exploration.