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.
> The "positive" surface already contains all the necessary points.
If this is the case then why are you allowed to duplicate the surface again on the "negative" plane? To me that gives the idea that you duplicate the whole original curve. He didn't motivate that step.
Or oh wait. I think I see it, a bit.
It's not so much duplication it's simply that by doing a negative visualization, you visualize it in a different way. But also in a way that relates to each other as the x,z plane are the same and the vertical (y) planes are inverted.
I guess one could say that the positive plane is for one midpoint and the negative plane for the other midpoint as the surface areas on those planes are a visualization of midpoints.
And then when you turn that into a klein bottle, you show how both midpoints relate.
If my understanding is correct enough, then I have to say, this is wild.
Thanks for explaining! This is really cool. Like I said, I'm not well-versed in math. To even have an understanding of following the main beats of it is really mindbending as most of it is new.
"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.
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).