Timeline for How do you motivate a precise definition to a student without much proof experience?
Current License: CC BY-SA 2.5
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| Mar 20, 2010 at 16:08 | history | made wiki | Post Made Community Wiki by Kim Morrison | ||
| Mar 20, 2010 at 13:19 | comment | added | Harald Hanche-Olsen | @Peter: So grant them the point. Introduce Lipschitz continuity and explore it a bit. It seems very natural, and the “right” definition until the students realize that the square root function is not Lipschitz. At which point you might introduce Hölder continuity, which seems to help, but now you have to keep track of the Hölder exponent instead. Finding the right definition is often a question of balancing the admission of pathological examples versus being too (arbitrarily) restrictive. | |
| Mar 20, 2010 at 3:28 | comment | added | Peter Arndt | Actually space filling curves might rather lead the students to the conclusion that the epsilon-delta-definition is not good because it includes such pathological examples. | |
| Mar 20, 2010 at 3:25 | comment | added | Yemon Choi | Unless I've misread the original question: it's not a course on proofs, but rather a course in which it is expected that most students will first encounter proofs. | |
| Mar 20, 2010 at 3:19 | history | answered | Harald Hanche-Olsen | CC BY-SA 2.5 |