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I was following until the very end. This felt very handwavy: >Now, since e is somewhere between 2 and 3, we have to conclude that n must be 2. Further, from ou
by Areibman 3y ago
I was following until the very end. This felt very handwavy:
>Now, since e is somewhere between 2 and 3, we have to conclude that n must be 2. Further, from our curve, we can see that there can only be one other value of x for which (lnx)/x = (ln2)/2, and since we know that 2⁴ = 4², we know that the other integer must be 4.
Is this sort of thinking something that could be justifiably written in a real proof? Sure, conveniently fishing out 2 as n seems to narrow down the search space for m, but I'd imagine this wouldn't work for harder problems
- ptspts 3y agoI think this part of the proof is precise. Which sentence is handwavy for you? “e is between 2 and 3” can be considered common knowledge, it easily follows from thd proof that its defining limit converges.
- archi42 3y agoThey say just before that: "Then we can say that 1 < n < e." Since e = 2.71..., there are not too many options for n. The sentence is a bit overconvoluted, but it's correct. Of course if the search space is bigger, you need to either do some more thinking to narrow it down - or spend a lot of time probing candidates.