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fabricebaudoin.blog | ||
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mkatkov.wordpress.com
For probability space $latex (\Omega, \mathcal{F}, \mathbb{P})$ with $latex A \in \mathcal{F}$ the indicator random variable $latex {\bf 1}_A : \Omega \rightarrow \mathbb{R} = \left\{ \begin{array}{cc} 1, & \omega \in A \\ 0, & \omega \notin A \end{array} \right.$ Than expected value of the indicator variable is the probability of the event $latex \omega \in... |
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mathbabe.org
A continuation ofthis, where I take notes on my workshop atHCSSiM. The real numbers are uncountable Today we used Cantor's diagonal argument to prove that the real numbers aren't countable. Namely, we assumed they were, and that we had a bijection $latex f: \mathbb{N} \rightarrow \mathbb{R}$ and then proved it didn't contain the real number... |
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dominiczypen.wordpress.com
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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www.casualoptimist.com
CartoonistVera Brosgol has posted her startling, wordless mini-comic What Were You Raised by Wolves? online. Read it in its entirety here. (via Robot 6) |
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