Comments by "betabenja" (@betabenja) on "Кривая Гильберта: полезна ли бесконечная математика?" video.

  1. surely the line, at the limit, does not hit every single point - surely, it only hits the rationals - not only that, only those with a power of 2 as a denominator?
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  2.  @3blue1brown  If I knew you were going to respond in person I'd have put a bit more effort into my random youtube comment. Your post does make sense. It's still a bit uncomfortable though, since the hilbert curve in the limiting value must have no gaps between the lines, which by definition it always does until you do it infinitely many times. I'd guess it's also similar to the idea that the an interval line can be fully created by placing a point at half way through and then two points half way between them to infinity. I've always felt that despite hitting all the points, it still doesn't equate to a line because it's still a collection of 0D points, which never would some how jump to a 1D entity when you have enough of them. I think I'm uncomfortable since, in the line version, the sum of the space between the points does not tend to 0 as the number of points tends to infinity, it never decreases, and is always the size of the line segment. Similarly, with the hilbert curve, the space between the curve on the 2D plane never decreases, even as the curve has more iterations. As the curve tends to larger, the space does not tend to 0. You end up with a curve that hits all the points in 2D but the space between those points is always the area of the 2D space you were trying to fill. It's like the limiting process does not work and you need to explicitly jump to infinity rather than tending to infinity to end up with that result.
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  3.  @3blue1brown  um. since you were gracious to answer in the first place please could you help my sanity by choosing from the following options: a) I'll get back to you, I've not read it, but might. b) you're still wrong, look up the definition of limits c) you might be right, deal with it, things get funky at infinity d) you might be right, I'm mulling it over e) I'm not going to get back to you f) I didn't expect some sort of spanish inquisition g) frankly, I didn't understand what you were saying h) 2pi i) see answer e) j) you sound like an engineer, so see answer i) k) I didn't get this far l) stop it m) blue! no wait, red! n) none of the above
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