Timeline for An Euler-proof that cannot be repaired?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jun 30, 2013 at 7:10 | vote | accept | CommunityBot | ||
| Jun 30, 2013 at 2:47 | comment | added | KConrad | Well, strictly speaking, by rearranging terms you'd get $\exp(\sum A_k/k) = \prod_p \exp(\sum 1/kp^k) = \prod 1/(1-1/p)$, which is $\sum 1/n$ by one argument or another. | |
| Jun 30, 2013 at 2:41 | comment | added | KConrad | @VivekShende: That's true. Since everything in sight is positive, convergence of $A_1$ would imply convergence of the harmonic series. | |
| Jun 30, 2013 at 2:36 | comment | added | Vivek Shende | As far as concluding $\sum 1/p = \infty$ goes, I don't understand what's wrong with Euler's original argument. If $A_1 = \sum 1/p$ was really finite, then nothing would stop us from expanding the finite quantity $\mathrm{exp}(\sum A_k / k)$ and getting $\sum 1/n$, contradiction. | |
| Jun 29, 2013 at 22:55 | history | answered | KConrad | CC BY-SA 3.0 |