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Post Closed as "not a real question" by Felipe Voloch, Mariano Suárez-Alvarez, Harry Gindi, Joel David Hamkins, Kevin Lin
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Background I'm interested in the issue of "explanatory" mathematical proofs and would like to try to find out what intuitions mathematicians have about induction, because there seems to be some disagreement as to whether such proofs can ever be explanatory. Question Does anyone have any proofs by induction that they think are particularly explanatory, and does anyone have any proofs by induction which they think fail to be explanatory at all? I'd be really grateful if you could post any examples, and also if you could say why you find it/don't find it explanatory. Thanks for your help. Comment I've just been reading through the comments and answers to my question and find them all very helpful. Thank you for taking the time to answer this question and post some interesting examples. Of course, more answers are still welcome! |
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Proofs by inductionBackground I'm interested in the issue of "explanatory" mathematical proofs and would like to try to find out what intuitions mathematicians have about induction, because there seems to be some disagreement as to whether such proofs can ever be explanatory. Question Does anyone have any proofs by induction that they think are particularly explanatory, and does anyone have any proofs by induction which they think fail to be explanatory at all? I'd be really grateful if you could post any examples, and also if you could say why you find it/don't find it explanatory. Thanks for your help.
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