Timeline for Field structure for R^n
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 10, 2010 at 12:36 | comment | added | Daniel Miller | I think that too many people forget the existence of bijections between R^n and R, and the interesting paradoxes one can derive from them. | |
| Dec 15, 2009 at 23:02 | comment | added | Harry Gindi | Downvoted for being obnoxious! | |
| Dec 15, 2009 at 19:56 | comment | added | Pete L. Clark | The way PW construed it is another standard problem: for instance, a variation on it it appears in Halmos' "automathography". It was honestly not clear to me what the OP intended. I think both answers are good. | |
| Dec 15, 2009 at 19:41 | comment | added | Qiaochu Yuan | This is clearly not the intent of the question. What you should've done is commented and asked for clarification on what properties of R^n the OP wanted preserved. | |
| Dec 15, 2009 at 19:32 | comment | added | Gerald Edgar | This is the real answer to the question actually asked. The OP didn't say it has to be an algebra over the usual R. He didn't say the multiplication has to be continuous in the usual toplogy of R. So (with axiom of choice) the additive group R^n is isomorphic to the additive group R, and we get the "yes" answer. | |
| Dec 15, 2009 at 19:00 | history | answered | Pierre Weil | CC BY-SA 2.5 |