Timeline for Has there been proposed an extension of real numbers that connects logarithms and exponents in closed form? [closed]
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Nov 18, 2016 at 3:02 | review | Reopen votes | |||
| Nov 18, 2016 at 6:30 | |||||
| Nov 13, 2016 at 21:38 | comment | added | Timothy Chow | Looks like a duplicate of mathoverflow.net/questions/237919/… (if you agree, please upvote this comment so that it appears "above the fold") | |
| Nov 13, 2016 at 13:30 | review | Reopen votes | |||
| Nov 13, 2016 at 14:10 | |||||
| Nov 13, 2016 at 10:06 | history | closed |
Bjørn Kjos-Hanssen abx Andrés E. Caicedo Franz Lemmermeyer Stefan Waldmann |
Needs details or clarity | |
| Nov 13, 2016 at 5:38 | comment | added | Anixx | @user44191 my question is whether something that connects exponents with logarithms in closed form has been already proposed by somebody. Not necessarily based on the user Survit's relation. | |
| Nov 13, 2016 at 5:33 | comment | added | user44191 | Essentially, this is the idea behind one form of nonstandard analysis - you can introduce infinitesimals, as long as you also introduce some idea of "round to a real number". | |
| Nov 13, 2016 at 5:28 | comment | added | user44191 | @Anixx : Let's assume we want your equation to work nicely under substitutions. Then: $\frac{(x^2)^\epsilon - 1}{\epsilon} = \log x^2$ Then $\frac{x^{2 \epsilon} - 1}{\epsilon} = 2 \log x$ Using the equation, we can rewrite this: $(\log x)(\epsilon \log x + 2) = 2 \log x$ And finally: $\epsilon (\log x)^2 = 0$ So assuming some nice idea of substitution, you get something that shouldn't work. You have to use some idea of "round to a real number" for this to work. | |
| Nov 13, 2016 at 5:04 | comment | added | Anixx | @Nate Eldredge By "connect" I meant "express in closed form". | |
| Nov 13, 2016 at 4:48 | comment | added | Nate Eldredge | Maybe it would help to try and state more precisely what "connect" should mean? | |
| Nov 13, 2016 at 4:45 | review | Close votes | |||
| Nov 13, 2016 at 10:06 | |||||
| Nov 13, 2016 at 4:31 | comment | added | Anixx | @Suvrit interesting hit, actually! I think it does not count per se, but can be a potential basis for contruction of a numerical system (for instance, adding such $\epsilon$ that $\frac{x^\epsilon-1}{\epsilon}=\log x)$. | |
| Nov 13, 2016 at 4:25 | comment | added | Suvrit | Does $\lim_{a\to 0} \frac{x^a-1}{a} = \log(x)$ count? | |
| Nov 13, 2016 at 4:11 | history | asked | Anixx | CC BY-SA 3.0 |