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by amitkgupta84
1652 days ago
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You just said it. The base case is true. The inductive case is wrong. You called it true “with sleight of hand”, but that’s more of a poetic statement; mathematically it’s simply wrong. One could write a completely different proof where the base case(s) cover n=1,2 and the inductive step is as in the post. In such a proof, the base case would be wrong and the inductive step would be correct. But that’s a different proof, not the one in the post. |
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Not really. H(1) is true. H(2) is false. But either one could be your base case.
The inductive step could be true or false, again depending on what you call your base case.