Induction Proofs, IV: Fallacies and pitfalls
نویسنده
چکیده
By now, induction proofs should feel routine to you, to the point that you could almost do them in your sleep. However, it is important not to become complacent and careless, for example, by skipping seemingly minor details in the write-up, omitting quantifiers, or neglecting to check conditions and hypotheses. Below are some examples of false induction proofs that illustrate what can happen when some minor details are left out. In each case, the statement claimed is clearly nonsensical (e.g., that all numbers are equal), but the induction argument sounds perfectly fine, and in some cases the error is quite subtle and hard to spot. Try to find it!
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