You only need to buy it at the airport if you want a Welcome Suica. You can buy a regular Suica at any station with a multi-function machine.
The only real differences between the Welcome Suica and a regular one are the 500 yen deposit (Welcome Suica doesn't require a deposit) and the limited validity (Welcome Suica automatically expires after about a month).
These sequences are also known as "cubefree," so you might want to continue researching along those lines.
In particular, the game discussed is trying to find cubefree words over a two-letter alphabet. The sample infinite game seems to agree with the listed sequence on OEIS for the lexicographically earliest infinite cubefree word, though your method of generation appears to be different from the one in the comments. (I haven't analyzed it in detail.)
The "positive" surface already contains all the necessary points. It's hard to prove that this surface on its own intersects with itself, but turning it into a Klein bottle makes the proof easy, since it's already known that the Klein bottle must intersect with itself when embedded in 3-D space.
It takes some rigor to ensure that mirroring the surface and turning it into a Klein bottle doesn't introduce a problem that would invalidate the proof, but the idea is this:
1) The surface exists only in the "positive" area above the x-y plane, and the mirror exists only in the "negative" area below the x-y plane.
2) The two surfaces only share the points on the original curve (on the x-y plane), and these points correspond only to the trivial cases where A=B. The surface and its mirror don't intersect anywhere else.
3) The resulting combined surface is a Klein bottle in 3-D space, which must intersect somewhere. Because of 2), that intersection must either be in the positive space or the negative space. Either way, that means there is an intersection in the original surface.
As briefly mentioned in the video, it's critical that the original constructed surface is only in the positive area, because otherwise when you mirror it and then turn it into a Klein bottle, the required intersection might just be the surface intersecting with the mirror, and not within the original surface itself.
"Confession" is fine as a translation. 告白 can be used for admitting to crimes, confessing one's love, revealing a secret, etc. It would never be used for a declaration where there is no sense of guilt/shame/embarrassment involved.
I tried searching to see what I could find, and it seems like the channels are run by a Korean living in Japan. (I suppose it could be multiple individuals)
Not all fonts are monospace. For example, on Windows you have MS PGothic and MS PMincho, which are the proportional versions of MS Gothic and MS Mincho.
It's a lot of different kinds of stationery in the form factor of a card, presumably for easier portability. For example, the top of the list has a ballpoint pen and a mechanical pencil that can be removed from the card. The third on the list has scissors, a cutter, and a paper punch.
This might be pedantic, but your rewriting seems to assume intent where there may have been none. The phrase "in such a way" is adverbial, modifying "surmounted" in the original, but your "designed" is adjectival, modifying "casing."
Since the casing is supposed to be malleable, it might not have necessarily been designed to line up the bearings, and it was only through a particular way of surmounting the casing that got them lined up.
One problem with grapheme clusters as length is that you can't do math with it. In other words, string A (of length 1) concatenated with string B (of length 1) might result in string C that also has length 1. Meanwhile, concatenating them in the reverse order might make a string D with length 2.
This won't matter for most applications but it's something you may easily overlook when assuming grapheme clusters are enough for everything.
You mentioned a studio/1br, which you can totally do in Tokyo under $2k, including food and other daily expenses. However, it will largely depend on what you consider a decent social life.
Publishers definitely don't see it that way; that's mostly an extension of a myth in order to justify the piracy.
Most manga publishers will see relatively little revenue from international anime releases. Even for domestic anime releases of the vast majority of titles, the manga publisher is only a small part of the anime production committee, and the hope is mostly that popularity of the anime can lead to increased sales of the manga, merchandise, or other events. So when the anime is released internationally, they get an even smaller cut of that because the international licensee also has to take their profit.
But other than mega-hit titles where an international anime release may also lead to significant international manga sales, the popularity of an anime adaptation overseas is practically irrelevant to the original manga publisher.
They get plenty of takedown notices, but they mostly get to hide behind services like Cloudflare who won't take action regarding these notices anyway. From the publishers/creators side, there is simply no effective way to take scanlators down.
Just to note, technically you can buy resin with money (you can replenish your resin with primogems, up to 6 times a day), but it's not very cost efficient so you're generally better off using those primogems on wishes. And like you said, you eventually run out of things you'll want to spend extra resin on.
Being unable to maximize a specific character's potential is pretty far from where you said "there are certain important ways in which you simply cannot progress without spending money."
There's nothing in the main content that requires you to have a 5* character/weapon, even though it's certainly easier with them.
It's generous enough if you aren't aiming for every premium character. If you play all the story content and events, and are doing the daily quests, you'll pretty much earn enough for a guaranteed 5* (80-90 pulls) in about 6 weeks (the length of one version update).
So if you're a free player, you can save up for a character you really want, or just pull and be content with whoever you get.
Unless you can point out where the statistics say that, your belief is just speculation. I've skimmed over the data and didn't see anything about attributing depression to work problems. (If you have other sources regarding this, please link them.)
Table 2-3 shows the breakdown of "health problems," and depression is at about 40%. Even if all of those were due to overwork, this is only 40% of the "health problems" category, which is not enough to support a claim that "most suicides come from excessive work." For sure, there may be many cases that do, but there are no clear numbers in that regard. Personally, I feel such claims only reinforce the typical stereotypes about Japan rather than try to understand the actual situation.
The leading reason for suicide is, by far, health problems. After that, you have economic/living situation, then domestic problems, then work-related problems ranking 4th.
Obviously, there could be overlap in some situations, but I think it's clear that "most" suicides do not stem from excessive work.
The only real differences between the Welcome Suica and a regular one are the 500 yen deposit (Welcome Suica doesn't require a deposit) and the limited validity (Welcome Suica automatically expires after about a month).