Glerk Pizza

Profile image description: Blue kris deltarune
Header image description: Cheese #709

ZFC: Probably inconsistent ngl
Birthdate: 22nd October 2019

Last Notes

2026-10-04 08:46:24 UTC

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hasnt anybody tried eating them? how do they taste?

2026-09-19 19:37:41 UTC

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when is chapter 4 coming out? reading this was interesting even though im not learning chinese

2026-09-19 14:40:35 UTC

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oh so that's why it's much simpler in the case of bivectors? because n choose 2 is always smaller than n^2? it's cool how i this algebraic problem turns out to be related to combinatorial things

2026-09-19 13:52:40 UTC

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i guess it intuitively makes sense, but how come the space of orbits of the action of an n dimensional group on a m dimensional space is dimension m - n? like how does one prove it?
@npub1nf4…nqe4 @npub1s7t…xfa0

2026-09-19 11:03:13 UTC

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when you said "The case n = 3 and n = 9 is interesting" did you mean to say "The case k = 3 and n = 9 is interesting"?

2026-09-19 09:17:45 UTC

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yay, is this geometric algebra? I've always wanted to learn more after seeing that one freya holmer video

2026-02-09 16:34:12 UTC

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Oh, now I remember; First of all, in the fact, by "field" I meant Kock field: A local ring where ∀𝑎. ¬(𝑎 = 0) → 𝑎 is invertible (n.b. this is not a geometric statement!. And the fact is thanks to Ingo Blechschmidt (for example they mention it in slide 20 of https://www.speicherleck.de/iblech/stuff/slides-padova2018.pdf, and it;s probably in her thesis too.
And apropos your second paragraph, the definition of field you gave (for each element a, either a = 0 or a is invertible) is the definition of a "discrete field" (also called geometric fields.
This is not as commonly used, because constructively, not many fields other than the rational numbers are discrete, not even the real numbers (without LPO. The more commonly used notion constructively is a Heyting field (a local ring where ∀𝑎. ¬(𝑎 is invertible) → 𝑎 = 0, which isn't a geometric statement. And there are a lot of other definitions of field, too, which are classically equivalent.
On the other hand, the geometric definition of being a local ring is satisfied constructively by pretty much everything you'd expect it to, (which is probably at least partially why topos theorists prefer it
@npub1q3d…vjr7 @npub1jxf…0dxv

2026-02-08 16:22:36 UTC

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I think I was thinking of something else.. I have not been able to find where I read it, so I'll sketch the argument from memory:
@npub1jxf…0dxv wanted to know if you could reconstruct all the maps R → S given only the maps R → k for a field k. More generally one could ask for a way to reconstruct a functor Ring → Set given only its restriction to fields F : Field → Set. As you showed, this is not possible. But the idea was that if your definition of F was constructive (valid internal to a topos), you could use the fact (?) that the affine line 𝔸¹ is a field in the internal logic of Sheaf(Ringᵒᵖ), so that applying F to it gives you a object of Sheaf(Ringᵒᵖ) and hence a functor Ring → Set which extends F.
Also, I'm pretty sure the place I read this from was in this week's finds; @npub1nf4…nqe4 does my description ring ring a bell?

2026-02-05 16:28:21 UTC

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I vaguely remember a solution to this which involved the internal language of the big Zariski topos, i don't remember the details though i think i rember @npub1nf4…nqe4 mentioning it in this weeks finds

2026-01-26 15:03:31 UTC

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The quoted post is unavailable, what was it?

2025-12-25 16:25:06 UTC

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No, thats not right - The diminished second is ♭♭2 (as is mentioned in the wikipedia article you linked), so it's enharmonic to the 1 (in 12TET at least). Musicians DO indeed call♭2 the minor second. (the rest is correct, i think)
https://en.wikipedia.org/wiki/Minor_second
[@counting_is_hard](https://mathstodon.xyz/@counting_is_hard ) @npub1zz2…9mhx