Julian Rosen
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 Apr 30 comment Polynomial roots in the ring extension The issue with the polynomial ring $R[x]$ is that $x$ commutes with elements of $R$, and there is no reason a root of $f$ should commute with $R$. Would it work to start with the free non-commutative algebra in one generator over $R$ (I think we can construct this as the set of finite sums of elements $r_1 x^{n_1}\ldots r_k x^{n_k}$, modulo the necessary relations), and quotient by the two-sided ideal generated by $f(x)$? Apr 30 answered Books about harmonic numbers Apr 30 answered Denominators of harmonic numbers: asymptotic behaviour. Apr 29 awarded Nice Answer Apr 25 awarded Pundit Apr 23 comment Are we allowed to compare infinities? The OP's question was not specifically about cardinality. The question is about comparing infinities, and there are several ways to do this. Apr 23 comment Are we allowed to compare infinities? Comparing densities is a natural way to compare sizes of infinite sets of integers. Apr 22 answered Are we allowed to compare infinities? Apr 11 answered A closed form for a lot of integrals on the logarithm Apr 7 comment Which functions can be the resistance of a network? I intended that you only have one copy of each unknown resistor, but I am also interested in what happens if you have more than one. Apr 7 asked Which functions can be the resistance of a network? Apr 5 awarded Yearling Mar 30 comment Can we rediscover the category of finite (abelian) groups from its morphisms? I answered the linked question, for every $\sigma\in\widehat{\mathbb{Z}}$, we can define an automorphism $F_\sigma$ of the category of finite groups, taking $(G,\circ)$ to $(G,\circ^\sigma)$, where $x\circ^\sigma y:=(x^\sigma y^\sigma)^{\sigma^{-1}}$. All of these are isomorphic to the identity, though, so they don't give a counterexample to this question. Mar 30 awarded Revival Mar 30 answered Cogroup structures on the profinite completion of the integers Mar 30 comment Is torsion of a topological module closed? Crossposted at mathoverflow. I posted an answer there. Mar 25 comment Infinite primes (places) of a number field geometrically What you're asking for may be difficult because any $\mathrm{Spec}(\mathcal{O}_K)$ is already proper over $\mathrm{Spec}(\mathbb{Z})$ (it is finite). In particular, every map from $\mathrm{Spec}(\mathcal{O}_K)$ to a scheme that is separated over $\mathbb{Z}$ has closed image, so in particular no separated scheme can have $\mathrm{Spec}(\mathcal{O}_K)$ as a non-trivial dense open subset. Mar 2 answered Integral $I=\int \frac{dx}{(x^2+1)\sqrt{x^2-4}}$ Feb 29 reviewed Approve Is this statement true: a set is open if every point has a closed ball contained inside of the set Feb 26 awarded Nice Answer