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almostsuremath.com | ||
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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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xorshammer.com
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| | | | | Let $latex \mathrm{PA}$ be Peano Arithmetic. Gödel's Second Incompleteness Theorem says that no consistent theory $latex T$ extending $latex \mathrm{PA}$ can prove its own consistency. (I'll write $latex \mathrm{Con}(T)$ for the statement asserting $latex T$'s consistency; more on this later.) In particular, $latex \mathrm{PA} + \mathrm{Con}(\mathrm{PA})$ is stronger than $latex \mathrm{PA}$. But certainly, given that... | |
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mattbaker.blog
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| | | | | In my last blog post, I discussed a simple proof of the fact that pi is irrational. That pi is in fact transcendental was first proved in 1882 by Ferdinand von Lindemann, who showed that if $latex \alpha$ is a nonzero complex number and $latex e^\alpha$ is algebraic, then $latex \alpha$ must be transcendental. Since... | |
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placeholderapi.wordpress.com
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| | | "I recently wrote about the new MoarVM dispatch mechanism, and in that post noted that I still had a good bit of Raku's multiple dispatch semantics left to implement in terms of it" https://6guts.wordpress.com/2021/04/15/raku-multiple-dispatch-with-the-new-moarvm-dispatcher/ | ||
