I'm trying to show the path-connectedness of the Sierpinski carpet and so far all I got is that at any iteration the sides of the carpet are always gonna be there so if there is a path from a point to any edge then it should be path-connected. However, I can't seem to formulate such a path. Can anyone give a hint or guide me in the right direction?
2026-03-28 20:57:56.1774731476
Showing that the Sierpinski's Carpet is path-connected.
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