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www.logicmatters.net | ||
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dvt.name
Gödel's incompleteness theorems have been hailed as "the greatest mathematical discoveries of the 20th century" - indeed, the theorems apply not only to mathematics, but all formal systems and have deep implications for science, logic, computer science, philosophy, and so on. In this post, I'll give a simple but rigorous sketch of Gödel's First Incompleteness ... |
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neilmadden.blog
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... |
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rjlipton.com
Exponential-time algorithms running on large data Moshe Vardi is perhaps the world's foremost expert on the application of logic to practical computations. His paper "Reasoning about Infinite Computations" with Pierre Wolper won the 2000 Gödel Prize. Infinite computations may not seem practical, but the magic is in the finite machines that perform them, and how... |
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statisticaloddsandends.wordpress.com
Let's say we have a convex, differentiable function $latex f: \mathbb{R}^p \rightarrow \mathbb{R}$ and that we want to minimize it. In this previous post, we saw that a gradient descent step at time $latex t$ (from point $latex \beta^t$) could be viewed as the minimizer of a quadratic approximation of $latex f$ at $latex \beta^t$:... |
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