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xorshammer.com | ||
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www.jeremykun.com
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| | | | | This proof assumes knowledge of complex analysis, specifically the notions of analytic functions and Liouville's Theorem (which we will state below). The fundamental theorem of algebra has quite a few number of proofs (enough to fill a book!). In fact, it seems a new tool in mathematics can prove its worth by being able to prove the fundamental theorem in a different way. This series of proofs of the fundamental theorem also highlights how in mathematics there are many many ways to prove a single theorem... | |
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almostsuremath.com
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| | | | | Given a sequence $latex {X_1,X_2,\ldots}&fg=000000$ of real-valued random variables defined on a probability space $latex {(\Omega,\mathcal F,{\mathbb P})}&fg=000000$, it is a standard result that the supremum $latex \displaystyle \setlength\arraycolsep{2pt} \begin{array}{rl} &\displaystyle X\colon\Omega\rightarrow{\mathbb R}\cup\{\infty\},\smallskip\\ &\displaystyle X(\omega)=\sup_nX_n(\omega). \end{array} &fg=000000$ is measurable. To ensure that this is well-defined, we need to allow X to have values in $latex... | |
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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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statisticaloddsandends.wordpress.com
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| | | I just came across a really interesting and simple algorithm for estimating the number of distinct elements in a stream of data. The paper (Chakraborty et al. 2023) is available on arXiv; see this Quanta article (Reference 2) for a layman's explanation. Problem statement Let's state the problem formally. Let's say we are given a... | ||
