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juliawolffenotes.home.blog | ||
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alanrendall.wordpress.com
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| | | | | In a previous post I discussed the Brouwer fixed point theorem and I mentioned the fact that it applies to any non-empty closed bounded convex subset of a Euclidean space, since a subset of this kind is homeomorphic to a closed ball in a Euclidean space. However I did not prove the latter statement. I... | |
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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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anuragbishnoi.wordpress.com
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| | | | | In the previous post, we saw the problem of determining the asymptotic growth of the function $latex T_L(n)$, which is the largest size of vector subspace $latex C \subseteq \mathbb{F}_3^n$, with the property that for any three distinct vectors $latex u, v, w$ in $latex C$, there is a coordinate $latex i$, such that $latex... | |
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thisfineplace.wordpress.com
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| | | Don't just escape from something; escape to something. Chris Guillebeau | ||
