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thehighergeometer.wordpress.com | ||
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dominiczypen.wordpress.com
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| | | | | Let $latex \omega$ denote the first infinite cardinal - that is, the set of non-negative integers. Let $latex p_0 = 2$ be the smallest prime number, and let $latex (p_n)_{n\in\omega}$ enumerate all prime numbers in ascending order. Let $latex \mathcal{U}$ be a free ultrafilter on $latex \omega$. We consider the field $latex F = \big(\prod_{n\in\omega}\mathbb{Z}/p_n\mathbb{Z}\big)/{\mathcal... | |
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jmanton.wordpress.com
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| | | | | If $latex Y$ is a $latex \sigma(X)$-measurable random variable then there exists a Borel-measurable function $latex f \colon \mathbb{R} \rightarrow \mathbb{R}$ such that $latex Y = f(X)$. The standard proof of this fact leaves several questions unanswered. This note explains what goes wrong when attempting a "direct" proof. It also explains how the standard proof... | |
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mikespivey.wordpress.com
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| | | | | The Riemann zeta function $latex \zeta(s)$ can be expressed as $latex \zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s}$, for complex numbers s whose real part is greater than 1. By analytic continuation, $latex \zeta(s)$ can be extended to all complex numbers except where $latex s = 1$. The power sum $latex S_a(M)$ is given by $latex S_a(M) =... | |
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jamesramseyteacher.wordpress.com
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| | | PROFESSIONAL LEARNING - HOW WE CAN APPLY EDUCATIONAL RESEARCH TO THE CLASSROOM? One of my main responsibilities as a Head of Learning Area is to create an environment where every teacher has a continuous desire to learn and improve. No matter how experienced or proficient a teacher is, everyone can improve. As Dylan Wiliam says... | ||
