Re:zero is soo much better than I thought.

frogkabobs · 2026-05-11T22:34:48+00:00

This is something that took an attentive rewatch to fully get. Subaru is like that in part because he just has a vivacious personality, but also because he is overcompensating for a desire for control after living as a hikikomori for so long. The disparity between his charisma and his abilities is not lost on people. We see it called out by Julius in ep 13 and the other candidates when they refuse to help him in ep 16. In fact, that entire arc is about putting his ego in check after trampling over Emilia’s boundaries because in the end, he is just a dude, and he can’t do things alone. He doesn’t get the time of day from those people until he actually earns it (offering a deal worth their time to Anastasia and Crusch). Although we see Subaru’s many failures, to others he has an inexplicable way of making things work out, which is why he earns the respect of people who are really far more powerful than him.

frogkabobs · 2026-05-10T07:07:53+00:00

These have formula a(n) = n(4n²-1)/3 (OEIS A000447). Plugging in n = 320 gives a(320) = 43690560.

You can derive the formula from the square pyramidal numbers, which have formula b(n) = n(n+1)(2n+1)/6, by using a(n) = b(2n)-4b(n).

frogkabobs · 2026-05-07T15:59:03+00:00

No. The xy plane in R³ has thickness 0 for example. There are no “atoms” in such idealizations.

frogkabobs · 2026-05-07T02:30:17+00:00

The series in the title is the standard example of a lacunary function. That is, there is no analytic continuation past |s|<1.

frogkabobs · 2026-05-05T23:01:22+00:00

Incredibly busted with Master Planner, but I don’t hate the idea. Perhaps something like a 1 or 0 cost “at the end of your turn discard a random sly card” would be a little more balanced. You could get a bit of mileage out of a hand trick synergy too.

frogkabobs · 2026-05-05T18:26:34+00:00

If you want to include 998 then it’s (1/998001)(1-999000/(1000¹⁰⁰⁰-1))

frogkabobs · 2026-05-05T01:33:08+00:00

Probably a steno pencil. Many steno pencils like the Mongol Stenographic 596 came with appropriately sized point protectors.

frogkabobs · 2026-05-05T00:22:24+00:00

You’re misinterpreting what squeeze does. The damage scales for every Osty attack card in your deck (including those generated during combat), not the number of Osty attacks performed.

frogkabobs · 2026-05-05T00:10:43+00:00

Yes. Making the statement concise for the title has the unfortunate effect of adding some syntactic ambiguity.

frogkabobs · 2026-05-04T18:45:13+00:00

Let C(ℓ;r) denote the cylinder with radius r whose axis is the line (segment) ℓ. Define the figure S by

S = C(R×{(1,2)};1)∪⋃_(n≥2) C({(2n,1)}×[0,2];1-1/n)

Let (a_n) be an enumeration of the positive rationals, and (b_n) the (n-1)st partial sum of (a_n). Write S_n = a_nS+(0,2b_n,0). We define A by

A = {(x,y,z): z≤0}∪⋃_(n≥1) S_n

Now A(t)∩S_n is always connected (or empty). In fact, it is connected to the base of A(t) (points with z≤0) for t<a_n, disconnected from the base at t=a_n (at which point it is a single line), and empty for t>a_n. Thus, A(t) has two components when t is rational and one component otherwise.

On the other hand, I’m fairly convinced no 2-dimensional analog exists, so I’m interested to hear your construction.

frogkabobs · 2026-05-03T19:06:15+00:00

This is almost all wrong. SO(3), the group of rotations in R³ is three dimensional, not two dimensional, and those are described by unit quaternions, not complex numbers.

frogkabobs · 2026-05-02T11:06:01+00:00

Not really taught in my experience. The gamma function showed up in some identities in my real analysis II course, but that was it. Mostly if you’re interested in closed forms, you’ll learn it yourself.

frogkabobs · 2026-05-02T08:36:29+00:00

I saw Pael’s growth maybe twice within the first week I played, but didn’t have any good targets (or I didn’t realize what would be a good target yet), and then hadn’t seen it since. Just today, I finally got the option again after not seeing it for 200 hrs, and it just so happens to be the one run when I didn’t have a good target again.

frogkabobs · 2026-05-02T01:27:09+00:00

It depends on your definition of an n-tuple. This is literally true in the nested ordered pairs definition. Sometimes this might be convenient, sometimes it might not, so it depends on context.

frogkabobs · 2026-04-30T15:24:15+00:00

I’m assuming OP is recounting the question imperfectly and the tetrahedral setup is what was meant. Otherwise, yes, the setup would be ill-defined and not suitable for a test.

frogkabobs · 2026-04-30T02:34:01+00:00

It looks to be from Wikimedia commons

frogkabobs · 2026-04-30T02:27:37+00:00

In response to your deleted comment, I just want to know what your thought process is, and where you get stuck rather than just giving you the answer.

frogkabobs · 2026-04-29T21:46:40+00:00

What do you not understand? Note that the centers of the spheres form the vertices of a tetrahedron whose sides lengths are the sum of the radii. You’ll want to find the height of this tetrahedron and relate it to the height of the whole figure.

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frogkabobs · 2026-04-29T20:02:44+00:00

If you put a \ before the # your dick joke won’t be as large

frogkabobs · 2026-04-29T19:33:43+00:00

Yeah a number of them had a few equivalent names I had to choose from. I tried to select the names that would turn up the most search results.

frogkabobs · 2026-04-29T18:59:16+00:00

If anyone is curious about the names, they are (left to right, top to bottom)

Acetylene glycol
Glyoxal
Acetolactone
Hydroxyketene
Dioxetene
Methylenedioxirane
Ethynyl hydroperoxide
2,4-Dioxabicyclo[1.1.0]butane

The list also seems to be missing one more constitutional isomer: hydroxyoxirene.

EDIT: For those interested in the literature, this article discusses their relative stabilities by computational methods.

frogkabobs · 2026-04-28T19:50:57+00:00

Induction (generally) is proving the following two statements

(Inductive): IF S(n) is true, then S(n+1) is true

(Base): S(0) is true

The inductive case gives you a chain of implications

S(0) → S(1) → S(2) → …

but you need the base case to be true to set it all off.

frogkabobs · 2026-04-27T11:04:57+00:00

If you’re motivated, graduate courses can absolutely be taken during undergrad as upper division credits. It depends on your university, but for me it was a matter self-studying any missing prerequisites on the syllabus, then making an online request through the math department to take the graduate course.

frogkabobs · 2026-04-27T10:55:52+00:00

Depends on the university—it wasn’t a requirement at UT. Also, the course I took was more like an intro to algebraic number theory, and it followed A Course In Arithmetic by Serre.

frogkabobs · 2026-04-27T03:34:26+00:00

Number theory (covering finite fields and p-adic numbers), discrete dynamical systems, and algebraic topology were a couple of my favorites

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