Timeline for What are your favorite instructional counterexamples?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 11, 2017 at 14:21 | comment | added | David Handelman | This boils down to the use of ${\bf N}$ to denote the positive integers (my use) or the nonnegative integers (your use); I prefer using $\bf Z^+$ for the latter, which avoids some ambiguity ... (and although it is nonstandard, $\bf Z^{++}$ for the positive integers avoids more ambiguity). | |
| Feb 11, 2017 at 14:13 | comment | added | Todd Trimble | Well, I say there is an $e_0$ because $0$ is a natural number (belongs to $\mathbf{N}$). But it's not important here. | |
| Feb 10, 2017 at 14:08 | comment | added | David Handelman | Easier is $T^* : e_i \mapsto e_{i-1}$ if $i > 1$, and $T^*e_1 = 0$ (there is no $e_0$). | |
| Feb 9, 2017 at 22:46 | comment | added | Todd Trimble | @GerryMyerson For (a) one doesn't have to be so fancy, but it could be the ring of bounded linear maps taking $l^2$ to itself, with multiplication given by composition. Here $y$ would be given by $T$, and $x$ by $e_0 \mapsto e_0$ and $e_{i+1} \mapsto e_i$. | |
| Feb 9, 2017 at 22:01 | comment | added | Gerry Myerson | Where is the ring? | |
| S Feb 9, 2017 at 21:43 | history | answered | David Handelman | CC BY-SA 3.0 | |
| S Feb 9, 2017 at 21:43 | history | made wiki | Post Made Community Wiki by David Handelman |