Timeline for Is it always possible to calculate the limit of an elementary function?
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
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| Mar 20, 2018 at 15:41 | comment | added | Gro-Tsen | @Olivier Oh now this is getting even more confusing. I give up! 😀 | |
| Mar 20, 2018 at 15:08 | comment | added | Olivier | @Gro-Tsen but then I'm confused by the relation to your problem just to clarify: olivier asked this question, while I'm Olivier (not at all the same MO user). | |
| Mar 20, 2018 at 14:14 | comment | added | Gro-Tsen | @Olivier I too am confused by the apparent conflict between IgorRivin's answer and the Richardson paper. I think the trick is that one merely purports to decide equality whereas Wang's paper refers to statements with an existential quantifier, but then I'm confused by the relation to your problem. I wish someone could clarify what can and what cannot be done (maybe this is grounds for a new question). | |
| Mar 20, 2018 at 8:57 | comment | added | Olivier | As someone rather ignorant both in analysis and in logic, I find this question and its answers 1) very interesting and 2) quite mysterious. Can someone clarify for instance how the answer of @IgorRivin is compatible with Schanuel's conjecture in the MO question quoted by @Gro-Tsen? I'm guessing that all potential zeros of polynomial and sine functions are not elementary zeros in the sense of Richardson. Am I right? | |
| Mar 20, 2018 at 6:14 | history | edited | Olivier Esser | CC BY-SA 3.0 |
added 178 characters in body
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| Mar 20, 2018 at 0:54 | answer | added | Igor Rivin | timeline score: 6 | |
| Mar 19, 2018 at 17:14 | comment | added | Gro-Tsen | You might be interested in the following related question: mathoverflow.net/q/118972 | |
| Mar 18, 2018 at 18:01 | history | edited | Olivier Esser | CC BY-SA 3.0 |
Add clarification as asked in the comments
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| Mar 17, 2018 at 16:38 | comment | added | Alexandre Eremenko | @oliver: If you are interested in real limits, see my answer part 2. However I am not 100% sure about the answer with complex limits. A singularity of an elementary function may not be isolated, so classification "removable, essential, ramification point" is not applicable. One needs some more sophisticated argument. | |
| Mar 17, 2018 at 15:49 | answer | added | Alexandre Eremenko | timeline score: 33 | |
| Mar 17, 2018 at 15:29 | comment | added | Olivier Esser | @ Alexandre Eremenko. My question concerns the reals. A comment on the original question asked on "math stack exchange" already did notice that the answer is true in the complex plane. But this result does not appear to transfer for real defined functions. Many "counter-example in analysis" do not exists anyway in complex analysis (smooth non-analytical function, etc.) | |
| Mar 17, 2018 at 15:09 | comment | added | Alexandre Eremenko | In your limit, $x\to a$ you admit all complex $x$ or only real? If complex, then $a$ can be only an algebraic singularity (a branch point pole, no worse), and then the limit can be always found by l'Hospital rule. | |
| S Mar 17, 2018 at 10:57 | history | suggested | Mateusz Kwaśnicki |
fixed a typo in a tag
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| Mar 17, 2018 at 10:49 | comment | added | YCor | If I understand correctly, the "elementary" class is not supposed to be closed under local inversion. I don't know if it matters, though. | |
| Mar 17, 2018 at 10:48 | review | Suggested edits | |||
| S Mar 17, 2018 at 10:57 | |||||
| Mar 17, 2018 at 10:41 | history | edited | YCor |
edited tags; edited tags
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| Mar 17, 2018 at 10:11 | review | First posts | |||
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| Mar 17, 2018 at 10:06 | history | asked | Olivier Esser | CC BY-SA 3.0 |