Comment by Gro-Tsen on Interesting examples of vacuous / void entities
I am trying to get chemists to accept the idea that the periodic table should start at element zero (nilium, having zero protons and zero electrons), in the noble gas column (which should be at the...
View ArticleComment by Gro-Tsen on What's the current longest snake-in-the-box in 10...
@CorentinB The 370 appears to be from Kinny, “A New Approach to the Snake-In-The-Box Problem”, Frontiers in AI and Applications242 (2012) 462–467: I don't have access to the paper, but the abstract...
View ArticleComment by Gro-Tsen on Why did Bourbaki's Élements omit the theory of...
@TimCampion Serre claims that flat cohomology can (might? could? he's not entirely clear) on the choice of the universe (unlike étale cohomology), so “even Deligne” (says Serre) is afraid to use it....
View ArticleNote rejected from arXiv: what to do next?
Short version: A note of mine was rejected by the arXiv moderation (something I didn't even know was possible) on account of being “unrefereeable”. The moderation process provides absolutely no...
View ArticleComment by Gro-Tsen on Cesàro convergence of Fourier series for $f \in...
Here are two possible precise references for this very standard fact: Antoni Zygmund, Trigonometric Series, 3rd ed., III.3.9 (vol. 1, p. 90); or Yitzhak Katznelson, An Introduction to Harmonic...
View ArticleComment by Gro-Tsen on Properties of a set of infinitely stacked regular...
I think the standard term here, insofar as there is one, for your repeated stacking operation is “Steinhaus [tetrahedron] chain”. Related to your conjecture 1, there is a proof of the fact that no...
View ArticleComment by Gro-Tsen on Algebraic structure, defined by its own automorphism...
Related question about when $\operatorname{Aut}(\operatorname{Aut}(A)) = \operatorname{Aut}(A)$.
View ArticleComment by Gro-Tsen on Does $\neg(j^{**}(\bot))=\neg\neg(j^{*}(\bot))$ hold...
Slightly related question
View ArticleComment by Gro-Tsen on What is known about sublocales defined by regular nuclei?
This answer proves incidentally that in a $\mathrm{T}_1$ topological space, the nucleus corresponding to any spatial sublocale is regular.
View ArticleAnswer by Gro-Tsen for Does $\neg(j^{**}(\bot))=\neg\neg(j^{*}(\bot))$ hold...
No, this does not hold in general. Here is a counterexample.Let $L := \mathcal{O}(\mathbb{R})$ be the frame of open sets in $\mathbb{R}$. Let $D$ be a dense subset of $\mathbb{R}$ whose complement $E...
View ArticleComment by Gro-Tsen on How close is the "bioctonionic projective plane" to an...
It's not clear (to me at least) what, if anything, Rosenfeld's projective plane for $\mathbb{C}\otimes\mathbb{O}$ has to do with the algebra in question (is it a mere analogy or is there a construction...
View ArticleComment by Gro-Tsen on For which sets do Arthur and Nimue have a winning...
@user14111 Indeed, if A+N have a winning strategy for $(P',Q')$ and $P\subseteq P'$ and $Q\subseteq Q'$, then A+N have a winning strategy for $(P,Q)$. I should probably have spelled this out explicitly.
View ArticleComment by Gro-Tsen on On the set of differentiability of a fat Cantor staircase
@NateRiver Sure, no problem. I can also provide higher resolution versions and/or the code used to generate them if this is useful.
View ArticleComment by Gro-Tsen on Can we “encrypt” in the Turing degrees?
@JeanAbouSamra I don't think this is true, however: for example, it is known that any $2$-generic and any $2$-random Turing degree form a minimal pair (that is, their inf is $\textbf{0}$), but there is...
View ArticleComment by Gro-Tsen on How big can determined sets be?
Can you, uh, refresh our memories on why $\omega_1 \hookrightarrow X$ implies that $X$ is not determined?
View ArticleComment by Gro-Tsen on Problems known to be in both NP and coNP, but not...
Since you mentioned it on social media, it might be worth adding here the news that this preprint (“Attractors Is All You Need: Parity Games In Polynomial Time” by van der Heijden) claims to prove that...
View ArticleComment by Gro-Tsen on Does the airplane Julia set contain true circles?
Experimentally (zooming in with a graphical Julia set computing program that I wrote) ages ago, the right edge of the central “circle” is at $\sim 0.109650026$ to within $10^{-9}$, whereas the top edge...
View ArticleComment by Gro-Tsen on Is van Dalen’s “open problem” about $\bf{CT}$ and...
Regarding your question of the relation between CT and omniscience principles, I think this needs to be a separate question (and you will need to make clear exactly what you mean by CT because there...
View ArticleComment by Gro-Tsen on If $X'$ computes $\mathcal{O}^{Y}$ must $X$ compute $Y$?
@PeterGerdes Could you provide a reference or statement to what you call “Spector's jump inversion”? I can't find anything by that name anywhere. (Or is “Spector” meant to be “Cooper”?)
View ArticleComment by Gro-Tsen on Why does the Fourier transform of $μ(n)/n$ look like...
@DanielWeber Excellent idea! I generated 4 random “control” curves with “fake” $\mu$ functions that coincide with $\mu(n)$ for $n\leq 12$ (I think $100$ is too much, so I went with $12$) and otherwise...
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