Timeline for Transcendence on $ \alpha+f(\alpha), \alpha f(\alpha) $ and $ \alpha/f(\alpha) $ where $ \alpha$ is transcendental
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| S Jun 20, 2021 at 2:20 | vote | accept | Beta | ||
| S Jun 20, 2021 at 2:20 | vote | accept | Beta | ||
| S Jun 20, 2021 at 2:20 | |||||
| Jun 20, 2021 at 2:19 | vote | accept | Beta | ||
| S Jun 20, 2021 at 2:20 | |||||
| Jun 19, 2021 at 17:03 | answer | added | Gabe Conant | timeline score: 3 | |
| Jun 19, 2021 at 15:55 | review | Close votes | |||
| Jun 25, 2021 at 3:03 | |||||
| Jun 19, 2021 at 15:20 | comment | added | Salvo Tringali | Really, why don't you start a new thread? This is a totally different question that the original one... | |
| Jun 19, 2021 at 14:35 | history | edited | Beta | CC BY-SA 4.0 |
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| Jun 19, 2021 at 14:30 | comment | added | Beta | I'm sorry, that sentence is not a precise description. What I want to ask is something like this: if $\alpha$ is transcendental, then are $\alpha+\cos(\alpha)$, $\alpha\cos(\alpha)$ and $\alpha/\cos(\alpha)$ transcendental? | |
| Jun 19, 2021 at 14:22 | history | edited | Beta | CC BY-SA 4.0 |
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| Jun 19, 2021 at 11:41 | comment | added | Salvo Tringali | You write that $f$ being "a real transcendental function with algebraic coefficients" means, for example, that "if $f(x)$ involves $\sin$ and $\cos$, then $f(x)$ is a polynomial in $\sin x$, $\cos x$ and $x$ with nonzero algebraic coefficients". But this is not the standard definition of a real transcendental function (and, to be honest, makes little sense whatsoever): Isn't the function $f: \mathbf R \to \mathbf R \colon x \mapsto \sin^2(x) + \cos^2(x) + x$ a "polynomial in $\sin x$, $\cos x$ and $x$"? | |
| Jun 19, 2021 at 11:25 | comment | added | Salvo Tringali | Dear 好きな人がいません: Your question keeps changing from version $n$ to version $n+1$ whenever you get a negative answer to version $n$. I start fearing that the process will never converge (let alone that doing something like this is considered, I think, unfair here on MathOverflow). If you have a new question, it could make more sense to post it on a new thread (after giving it enough of a thought). With that said, I don't understand what you're asking for in the current version of the OP: Isn't $\cos(\cdot)$ a transcendental function? | |
| Jun 19, 2021 at 10:46 | history | edited | Beta | CC BY-SA 4.0 |
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| Jun 19, 2021 at 10:22 | history | edited | Beta | CC BY-SA 4.0 |
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| Jun 19, 2021 at 10:15 | history | edited | Beta | CC BY-SA 4.0 |
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| Jun 19, 2021 at 9:29 | history | edited | Beta | CC BY-SA 4.0 |
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| Jun 19, 2021 at 9:14 | answer | added | Salvo Tringali | timeline score: 3 | |
| Jun 19, 2021 at 8:16 | history | asked | Beta | CC BY-SA 4.0 |