My gut tells me that if you took a vertical cross section of the Sierpinski carpet at an $x$-coordinate in the Cantor set, the cross section would again be the Cantor set. However, I'm at a loss for how to prove this (or even give a heuristic argument).
2026-03-29 03:36:05.1774755365
Does any cross section of the Sierpinski carpet yield the Cantor set?
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