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wildtopology.com | ||
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thehighergeometer.wordpress.com
Here's a fun thing: if you want to generate a random finite $latex T_0$ space, instead select a random subset from $latex \mathbb{S}^n$, the $latex n$-fold power of the Sierpinski space $latex \mathbb{S}$, since every $latex T_0$ space embeds into some (arbitrary) product of copies of the Sierpinski space. (Recall that $latex \mathbb{S}$ has underlying... |
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xorshammer.com
An arithmetic statement is one made up of quantifiers ``$latex \forall n\in\mathbb{N}$,'' ``$latex \exists n\in \mathbb{N}$,'' the logical connectives ``and,'' ``or,'' ``not'', function symbols $latex \times$, $latex +$, constants $latex {0}$, $latex 1$, and variables $latex n$ which are bound by the aforementioned quantifiers. It is known that there is no algorithm which will decide... |
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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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geriatrixfotogallerie.wordpress.com
52 Weeks Photo Challenge: Week 32 |
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