Timeline for Is nᵐ>mⁿ if m>n?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 7, 2017 at 21:18 | audit | Low quality posts | |||
| Sep 7, 2017 at 21:18 | |||||
| Aug 21, 2017 at 15:58 | comment | added | Pritt Balagopal | @MeniRosenfeld Ohh, so that's what it means. Thanks for patching it up | |
| Aug 21, 2017 at 15:08 | comment | added | Meni Rosenfeld | @PrittBalagopal: Are you sure you understood what this graph is saying? It shows the regions in which $n^m > m^n$. It answers your question negatively, as there are areas where $m>n$ and yet $m^n>n^m$ (the white area to the left). But if $n>e$ (that's the vertex point where the two shaded areas meet) you have $m>n \Rightarrow n^m>m^n$. | |
| Aug 21, 2017 at 11:25 | comment | added | Henry | This would benefit from a description of the boundary curves, one being $m=n$ and the other being the other solutions to $\dfrac{\log m}{m} = \dfrac{\log n}{n}$ with $m,n >1$, crossing at $(e,e)$ | |
| Aug 21, 2017 at 11:06 | comment | added | Pritt Balagopal | Thanks, but I already knew the graph. :) Anyway it'll be helpful for other users visiting this question from google. (+1) | |
| Aug 21, 2017 at 9:24 | history | answered | Raffaele | CC BY-SA 3.0 |