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xorshammer.com | ||
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almostsuremath.com
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| | | | | The aim of this post is to motivate the idea of representing probability spaces as states on a commutative algebra. We will consider how this abstract construction relates directly to classical probabilities. In the standard axiomatization of probability theory, due to Kolmogorov, the central construct is a probability space $latex {(\Omega,\mathcal F,{\mathbb P})}&fg=000000$. This consists... | |
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queuea9.wordpress.com
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| | | | | Parametricity is a profound principle in the theory of programming languages -- but what kind of principle is it? To answer this, let me first recall the idea, as introduced by the great John C. Reynolds in his seminal paper "Types, Abstraction, and Parametric Polymorphism". (I wrote about this paper in an earlier post.) Suppose... | |
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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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xorshammer.com
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| | | There are many functions from $latex \mathbb{N}$ to $latex \mathbb{N}$ that cannot be computed by any algorithm or computer program. For example, a famous one is the halting problem, defined by $latex f(n) = 0$ if the $latex n$th Turing machine halts and $latex f(n) = 1$ if the $latex n$th Turing machine does not... | ||
