Timeline for Uniqueness of the logarithm function
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| S Aug 2, 2023 at 22:25 | history | suggested | High GPA | CC BY-SA 4.0 |
fix two typos in Latex equations
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| Aug 2, 2023 at 15:51 | review | Suggested edits | |||
| S Aug 2, 2023 at 22:25 | |||||
| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
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| May 1, 2010 at 22:07 | vote | accept | Silva | ||
| Apr 27, 2010 at 15:37 | comment | added | Mark Meckes | The reason to introduce another function $g$ is merely to clarify what "unique" means. For the last few years I've been teaching students in the first or second proof-based math classes, and I've found that "unique" is one of the words mathematicians are most likely to take for granted and don't necessarily even try explain the meaning of, but that many students don't understand. | |
| Apr 27, 2010 at 14:10 | comment | added | Wadim Zudilin | If the proof shows that for a function $f(x)$ one has to have $f(x)=\sup A_x$ at each point $x$, then $f(x)$ is defined uniquely, so no need to introduce another function $g(x)$. But one can do, without changing the proof. | |
| Apr 27, 2010 at 13:01 | comment | added | Mark Meckes | As I understand the question, the answers below don't address the poster's confusion. The poster apparently understands the proof that $f(x) = \sup A_x$ already, but doesn't see why this implies uniqueness of $f$, probably due to not appreciating what "unique" means. So to clarify: saying that such an $f$ is unique means that if $f$ and $g$ are both increasing functions that satisfy 1. and 2., then $f=g$. The proof you outline implies this since it shows that for each $x$, $f(x)$ and $g(x)$ are both equal to $\sup A_x$. | |
| Apr 27, 2010 at 11:25 | answer | added | Wadim Zudilin | timeline score: 5 | |
| Apr 27, 2010 at 10:31 | history | asked | Silva | CC BY-SA 2.5 |