I was wondering why the Goedel's incompleteness theorem didn't apply to Euclidean geometry. After all we can encode natural numbers on a blackboard by drawing digits, which are geometric figures. Turns out the problem is that we can't pick the encoding using first order logic.
https://math.stackexchange.com/questions/90393/why-euclidean-geometry-cannot-be-proved-incomplete-by-g%C3%B6dels-incompleteness-the
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