Timeline for Is $\sum\limits_{k=0}^{\infty}\frac{1}{(mk)!^{n+1}}$ irrational?
Current License: CC BY-SA 4.0
19 events
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| Jan 24, 2023 at 13:20 | comment | added | fedja | @Frax at the same time considering Hitler the best candidate as the next USA president If it does not know who Hitler was, it should be smart enough just to say "I don't know who that is, so I cannot tell whether it is a good candidate or not"; if it does know who that was and still considers him a good candidate, then, apparently, its logic led to that conclusion and it should show that logic. Hitler, BTW, has a huge advantage over many other politicians: he is already dead. So in some elections I would certainly vote for him over both main candidates :-) | |
| Jan 24, 2023 at 12:07 | comment | added | Frax | @fedja Sad part is that it's necessary, as it may have prevented further optimization of chatGPB in general if it were capable of solving very difficult math problems while at the same time considering Hitler the best candidate as the next USA president... | |
| Jan 24, 2023 at 0:24 | comment | added | fedja | Wolfram Alpha is incapable of proving or disproving anything. Mainly it is just a symbolic manipulator, so unless it can reduce it to $e\sqrt 5$ or something else like that, it has no opinion about the irrationality of the number. On the other hand, chatGPT would be capable of doing such stuff by now if its creators hadn't wasted time on teaching it who Columbus was and how to appear nice and virtuous and answer clear and well-posed questions by long preaching about good and evil when the conversation makes a dangerous turn :-). | |
| Jan 23, 2023 at 16:08 | history | edited | YCor |
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| Jan 23, 2023 at 16:00 | comment | added | Frax | I changed the title and added one more example to generalize the point of my question. | |
| Jan 23, 2023 at 15:59 | history | edited | Frax | CC BY-SA 4.0 |
Changed title and added one more example to generalize my question
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| Jan 22, 2023 at 21:21 | history | edited | Frax | CC BY-SA 4.0 |
Correction.
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| Jan 22, 2023 at 18:19 | history | edited | Frax | CC BY-SA 4.0 |
Inverted order of some values for a more readable experience
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| Jan 22, 2023 at 18:14 | history | edited | Frax | CC BY-SA 4.0 |
Error in the proof: corrected.
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| Jan 22, 2023 at 15:23 | comment | added | Carl-Fredrik Nyberg Brodda | @CarloBeenakker Well, ChatGPT has given me several elementary proofs of Fermat’s last theorem, so I’d take anything it says about maths with a massive pinch of salt. | |
| Jan 22, 2023 at 15:12 | history | edited | Frax | CC BY-SA 4.0 |
added 5 characters in body
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| Jan 22, 2023 at 15:04 | comment | added | Frax | @GeraldEdgar isn't that a proof about the standard Bessel function of the first kind? Does it still work here (Modified one)? Genuine question | |
| Jan 22, 2023 at 15:00 | comment | added | Gerald Edgar | Proof here ... mathoverflow.net/a/103161/454 | |
| Jan 22, 2023 at 14:57 | history | edited | Frax | CC BY-SA 4.0 |
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| Jan 22, 2023 at 14:41 | history | edited | Frax | CC BY-SA 4.0 |
[Edit removed during grace period]
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| Jan 22, 2023 at 13:24 | comment | added | Carlo Beenakker | chatGPT doesn't know either... "It is not known whether the value of I_0(2) (Modified Bessel function of the first kind) is irrational or not. While some special values of the Bessel functions are known to be irrational, there is no proof that all values are irrational, and it is not known if there are any general methods for determining whether a particular value is irrational." | |
| Jan 22, 2023 at 12:33 | comment | added | username | Yes, your proof is (to my eyes) perfectly natural and correct. Is unknown an error ? It could be unknown to the person who wrote it. There are other mistakes of that type in Wolfram Alpha (I know of one with respect to the loosest sphere packing, which has been shown two decades ago to be arbitrarily close to zero,, and yet is still announced as 0,055%). | |
| S Jan 22, 2023 at 11:32 | review | First questions | |||
| Jan 22, 2023 at 13:11 | |||||
| S Jan 22, 2023 at 11:32 | history | asked | Frax | CC BY-SA 4.0 |