If you are so certain that there isn't an easy to find solution as to why this is wrong on the internet, wouldn't it be nice to add a follow up if no one in the comments gets the right reason? I'm sure you'll be able to provide the real, complete reason this doesn't work out.
yes of course :o) but first think about it yourself.
I just realized that the hint I gave is not good. I changed it to: Collect all the horizonal and vertical lines separately. Now it is much clearer.
I'm assuming that it has something to do with the fact that the unit line is one dimensional, as in, it has no "thickness", whilst the baby blue line is two dimensional and sort of covers an area. So even though it looks to us like the line is approximating the unit line, the approximation is always off by still having "thickness". But I'm not versed well enough in maths to concretely describe my thoughts on this. I don't even know if my idea is going in the right direction at all or if it's much simpler than that.
Yeah you are on the right track. The blue line has two directions. Take the sum of the length in each direction separately.
Well, the sum of the length in the horizontal direction needs to be 1, otherwise the whole thing wouldn't make sense. Leaving us with a vertical length of 2. I am not sure how this helps me though.
If you look back at the picture with the green and blue line. Imagine n goes to infinity are there still vertical lines left?
Of course there are, they are just infinitesimally small. Their sum doesn't change, it's still two.
My previous question was poorly phrased.
The blue line converges to the green line. But the green line has no length in the vertical direction. So where did all the vertical lines go?