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mikespivey.wordpress.com | ||
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mathematicaloddsandends.wordpress.com
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| | | | | The function $latex f(x) = x \log x$ occurs in various places across math/statistics/machine learning (e.g. in the definition of entropy), and I thought I'd put a list of properties of the function here that I've found useful. Here is a plot of the function: $latex f$ is defined on $latex (0, \infty)$. The only... | |
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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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dominiczypen.wordpress.com
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| | | | | The starting point of this blog post is a slight reformulation of the $latex T_0$ separation axiom: A topological space $latex (X,\tau)$ is $latex T_0$ if for all $latex x\neq y\in X$ there is a set $latex U\in \tau$ such that $latex \{x,y\}\cap U \neq \emptyset \text{ and } \{x,y\}\not\subseteq U.$ Given a cardinal $latex... | |
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ropmann.wordpress.com
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| | | Visit the post for more. | ||
