Timeline for Examples of interesting false proofs
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 2, 2021 at 23:40 | comment | added | Gerry Myerson | All limits are unique, but some limits are more unique than others. | |
| Sep 28, 2021 at 23:54 | comment | added | Andreas Blass | @AlessandroDellaCorte The more powerful technique, which I've seen too many students use, is to remember a slogan, like "uniqueness of limits" or some formula highlighted in the textbook, while forgetting the surrounding words, like the hypotheses that underlie the slogan. | |
| Sep 28, 2021 at 22:16 | comment | added | Alessandro Della Corte | That's a nontrivial generalization. From Solution to Exercise 1 = $L_1$ and Solution to Exercise 2 = $L_2$ he couldn't conclude $L_1=L_2$ with my proposed technique. I wonder which more powerful technique he used. | |
| Sep 28, 2021 at 21:16 | comment | added | Pietro Majer | Years ago a student came to me asking for clarifications on some exercises on limits I had left. “I did this limit and I got 1” I checked and said “Correct!”. “And then I did exercise 2 and I got 0”. I checked again and said “Correct!”. He said: “But doesn’t this contradict the uniqueness of the limit?” | |
| Apr 16, 2021 at 8:16 | comment | added | Francesco Polizzi | Yes, in fact my personal idea of "interesting false proof" is more something like "proof which is flawed for some subtle conceptual reason". But I understand what you mean. | |
| Apr 16, 2021 at 8:13 | comment | added | Alessandro Della Corte | You have a point, of course, and "interesting" is subjective. It seems so to me because I see students using notation this way all the time. In fact even some texbooks providing a correct proof of the above theorem start writing down something like that, so it seems a nice way to point out the incorrect use of the notation. | |
| Apr 16, 2021 at 8:00 | comment | added | Francesco Polizzi | Rather than an "interesting" false proof, this seems to me a notational ambiguity. Writing "$\lim_{x\to x_0} f(x)=L_1$" it seems that you are already assuming uniqueness, whereas (in general) limits can form a set with more than one element. | |
| S Apr 16, 2021 at 7:33 | history | answered | Alessandro Della Corte | CC BY-SA 4.0 | |
| S Apr 16, 2021 at 7:33 | history | made wiki | Post Made Community Wiki by Alessandro Della Corte |