Hi, I am confused by the following diagram when I try to understand it in terms of limit as done by Real-analysis: What I currently understand is as follows: Let the finite length of the straight orange line be X>0. The rest of the non-straight orange lines (in this particular case, the non-straight orange lines have forms of different degrees of Koch fractal) are actually the same line with finite length X>0, such that its end points are projected upon itself, and as a result we get the convergent series 2*(a+b+c+d+...) . Each one of the non-straight lines is constructed by 4n straight parts, where n is some natural number and the length of each part is X/4n, so given any arbitrary non-straight line, it has a finite amount of parts ( X=(X/4n)*4n ). By using limit as done by Real-analysis X-2*(a+b+c+d+...)=0, but 2*(a+b+c+d+...) is the projected result of finite amount of non-straight lines, where each one of them has the same finite length, which is X>0 (as observed above). 2*(a+b+c+d+...) (which is the result of the projection of a finite length X>0 upon itself) is equal to X only if a projected non-straight line somehow collapsed into length 0. This is definitely not the case in the diagram above (there are finitely many non-straight lines, where each one of them has the same finite length X>0). So, I still do not understand how X-2*(a+b+c+d+...)=0 by Real-analysis. Can I get some help?