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It is completely valid to do that. The induction starts at n=2. Nothing unusual about it, e.g. you can show that 2^n >10 for n>=4 that way.
by diffeomorphism 5y ago
It is completely valid to do that. The induction starts at n=2.
Nothing unusual about it, e.g. you can show that 2^n >10 for n>=4 that way.
- amitkgupta84 5y agoI mean “valid” in the mathematical/logical sense. It does not follow from the stated assumptions that n > 1, in the inductive step is this proof. This has nothing to do with the idea that it can be common practice to prove claims of the form for all n > N, P(n) by induction when N is a number like 4. Yes there is a perfectly valid way to use proof by induction to do such proofs. Has nothing to do with this blog post.
- shkkmo 5y agoIn a proof, you can absolutely assume something like "A is true", you do it as a part of a sub-proof. Then anything you prove in the sub-proof like "B is true" can be brought back into the main proof in the form: A implies B is true. The blog post glosses over this assumption and thus ends up concluding "p(n) implies p(n+1)" instead of "p(n) implies (n>1 implies p(n+1))”