Timeline for Examples of common false beliefs in mathematics
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 5, 2014 at 16:50 | comment | added | user9072 | While technically it is true one can do it with countably many for the function I gave (if one includes degenerate intervals) I would be surprised if not at least some (or rather most) of the confusion of the students could be addressed by the example (possibly continuing with discussion along the lines suggested by @AndresCaicedo). | |
| Jan 2, 2014 at 23:44 | comment | added | Andrés E. Caicedo | You can surely discuss fractal shapes without needing to go into the details of a technical counterexample. The point seems to be that it is hard to imagine that "increasing at a point" and "increasing in a neighborhood of a point" are not the same for continuous functions. You can give easy examples showing that indeed they disagree, locally, and fractals suggest that you can make the disagreement happen everywhere. You can revisit this later, once more technology has been set in place. | |
| Jan 2, 2014 at 19:17 | comment | added | Izhar Oppenheim | It is in the case of finitely many subintervals, but not in the case of countably many subintervals. | |
| Jan 2, 2014 at 17:33 | comment | added | user9072 | Why not $x \sin(1/x)$ as example? | |
| S Jan 2, 2014 at 15:41 | history | answered | Izhar Oppenheim | CC BY-SA 3.0 | |
| S Jan 2, 2014 at 15:41 | history | made wiki | Post Made Community Wiki by Izhar Oppenheim |