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>Physical measurements can have irrational lengths
ok this is just ridiculous. I'm just supposed to accept that a calculated shape has a length that never ends. You will always have some infinitely small opening on its calculated side. But if you actually made a 1x1 square and measured its diagonal length, even at the atomic level the length will end, proving its side length genuinely terminates. You can't have an irrational length and a closed object at the same time - this concept is fully contradictory and makes zero practical sense. Are you also saying that the circumference of a circle is never truly ever closed because Pi is irrational? An opening in a shape no matter how small it is, is still an opening. All shapes will "leak" if they have irrational side lengths which is retarded.

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