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Yeah, I don’t get how you distinguish between a correct visual proof and a visual proof that looks right but doesn’t actually prove what it’s trying to prove. Y
by wat10000 1y ago
Yeah, I don’t get how you distinguish between a correct visual proof and a visual proof that looks right but doesn’t actually prove what it’s trying to prove. You could probably make a pretty convincing-looking visual proof that the limit of the sum of the harmonic series is below some finite number, that 0.9 repeating is less than 1, that there are more rationals than integers, that there are the same number of reals and rationals, and that sort of thing.
On the linked page, a lot of the proofs are essentially proofs by induction that stop at some (pretty small) n. Maybe there’s a way to make it rigorous by visually showing the induction step that proves n+1 given n, but if there is, it’s not shown.
This can be great for building intuition for a statement known to be true by other means, but I wouldn’t consider them to be proofs.
- monktastic1 1y ago> Yeah, I don’t get how you distinguish between a correct visual proof and a visual proof that looks right but doesn’t actually prove what it’s trying to prove. This problem exists not only for visual proofs, but for standard written ones too.
- wat10000 1y agoNot in the same way. For a written proof it can be hard but with effort and sufficient background knowledge you can figure out if it actually proves the statement or not. If the proof doesn’t prove the statement there will be a step that doesn’t follow from the rest of it. You may not be able to spot it but it can at least theoretically be spotted.