Timeline for Are either $\pi + e$ or $\pi e$ transcendental if we add or multiply digit-wise? [closed]
Current License: CC BY-SA 4.0
37 events
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| Aug 29, 2019 at 5:10 | comment | added | Francois Ziegler | What does the preamble, which is about the usual sum $\pi+e$ and product $\pi e$, now have to do with the question about $\pi+_{10}e$ and $\pi\times_{10}e$? | |
| Jul 7, 2019 at 13:20 | review | Reopen votes | |||
| Jul 7, 2019 at 20:20 | |||||
| Jun 16, 2019 at 14:54 | comment | added | user141903 | Great idea Zach! | |
| Jun 15, 2019 at 17:28 | comment | added | Zach Teitler | Even simpler questions seem impossible. Just take the digits of $\pi$ or $e$ and reduce them, say, modulo $2$. So $\pi = 3.1415926536... \mapsto 1.1011100110...$. Is it transcendental? Irrational? | |
| Jun 15, 2019 at 12:29 | comment | added | user141903 | I edited the question, so I hope it is more clear. This is similar to another question I asked (though I had since deleted my account). | |
| Jun 15, 2019 at 12:25 | review | Reopen votes | |||
| Jun 15, 2019 at 18:26 | |||||
| Jun 15, 2019 at 12:23 | history | edited | user141903 | CC BY-SA 4.0 |
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| Jun 15, 2019 at 12:06 | history | edited | user141903 | CC BY-SA 4.0 |
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| Jun 15, 2019 at 12:05 | comment | added | user141903 | LSpace, thanks I thought it would be helpful but I see it is not :) I'll remove the image! | |
| Jun 15, 2019 at 11:59 | history | closed |
Francois Ziegler GH from MO Andrés E. Caicedo R.P. LSpice |
Needs details or clarity | |
| Jun 15, 2019 at 11:58 | comment | added | LSpice | Your question starts with someone else's explanation of your question in terms of two new operations $+_{10}$ and $\times_{10}$, and then immediately discusses the old operations $+$ and $\times$. It seems very confusing to me. I have inlined @NateEldredge's comment in favour of not forcing people to read a non-zoomable screenshot, but I left in the original screenshot too, since it seems necessary for understanding what you're saying. I encourage you to replace the screenshot by the text if it is consistent with your intention. | |
| Jun 15, 2019 at 11:57 | history | edited | LSpice | CC BY-SA 4.0 |
TeX fixes; inlining @NateEldredge's comment
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| Jun 15, 2019 at 11:09 | history | edited | user141903 | CC BY-SA 4.0 |
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| Jun 15, 2019 at 10:55 | comment | added | user141903 | Nate, that is a great notation! I like your explanation. | |
| Jun 14, 2019 at 8:29 | comment | added | Francois Ziegler | Oooh! I see now. What about $\sqrt 2+_{10}\sqrt 3$, $\sqrt 2\times_{10}\sqrt 3$? | |
| Jun 14, 2019 at 7:25 | comment | added | Nate Eldredge | @FrancoisZiegler: I believe the idea is to create two new operations, call them $+_{10}$ and $\times_{10}$, which come from identifying an element of $\mathbb{R}$ as a sequence of elements of $\mathbb{Z}_{10}$, $x \mapsto (\dots, 0, 0, \dots, a_n, a_{n-1}, \dots, a_0, a_{-1}, \dots)$, via the decimal expansion, and adding or multiplying componentwise. The question then is whether $\pi +_{10} e$ or $\pi \times_{10} e$ are (identified with) transcendental numbers. | |
| Jun 14, 2019 at 7:16 | comment | added | Francois Ziegler | “Either” $\pi+e$ or $\pi e$ is transcendental whether the pope is catholic or I am the queen of England. What is the question? | |
| Jun 14, 2019 at 6:16 | comment | added | Gerry Myerson | I bet they're all transcendental, and I bet I won't be able to collect on my bet. | |
| Jun 14, 2019 at 5:08 | history | edited | Martin Sleziak |
added the (digits) tag - feel free to edit the tags further if some of the ones I've added are not a good fit
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| Jun 14, 2019 at 5:04 | history | edited | user141903 | CC BY-SA 4.0 |
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| Jun 14, 2019 at 4:58 | history | edited | user141903 | CC BY-SA 4.0 |
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| Jun 14, 2019 at 4:58 | history | edited | Martin Sleziak |
added a top-level tag; https://meta.mathoverflow.net/questions/1457/why-are-mo-tags-formatted-as-they-are
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| Jun 14, 2019 at 4:57 | history | edited | user141903 | CC BY-SA 4.0 |
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| Jun 14, 2019 at 4:51 | history | edited | user141903 | CC BY-SA 4.0 |
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| Jun 14, 2019 at 3:25 | history | edited | user141903 | CC BY-SA 4.0 |
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| Jun 14, 2019 at 3:06 | review | Close votes | |||
| Jun 15, 2019 at 12:00 | |||||
| Jun 14, 2019 at 3:05 | comment | added | user141903 | Daniil, I'm sorry for the confusion. I'm saying add or multiply from $\pi$ and $e$ at each digit and then find the resulting number mod $n$ at every digit to get a new decimal number with an infinite length. | |
| Jun 14, 2019 at 3:02 | history | edited | user141903 | CC BY-SA 4.0 |
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| Jun 14, 2019 at 2:52 | comment | added | Daniil Rudenko | I am not sure that I understand your question. There certainly does not exist a way to understand whether a number is transcendental, looking at a finite number of digits. | |
| Jun 14, 2019 at 2:40 | history | edited | user141903 | CC BY-SA 4.0 |
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| Jun 14, 2019 at 2:31 | history | edited | user141903 | CC BY-SA 4.0 |
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| Jun 14, 2019 at 2:14 | comment | added | user141903 | Thanks Jose, yes I was thinking the same and corrected. | |
| Jun 14, 2019 at 2:13 | history | edited | user141903 | CC BY-SA 4.0 |
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| Jun 14, 2019 at 2:13 | comment | added | José Hdz. Stgo. | If both of them were algebraic over $\mathbb{Q}$, then both $\pi$ and $e$ would be algebraic over $\mathbb{Q}$, q.e.a. Thus, one of those two numbers is of necessity transcendental. | |
| Jun 14, 2019 at 2:09 | history | edited | user141903 | CC BY-SA 4.0 |
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| Jun 14, 2019 at 2:05 | review | First posts | |||
| Jun 14, 2019 at 4:56 | |||||
| Jun 14, 2019 at 2:03 | history | asked | user141903 | CC BY-SA 4.0 |