Timeline for Strong induction without a base case
Current License: CC BY-SA 2.5
27 events
| when toggle format | what | by | license | comment | |
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| Dec 24, 2010 at 22:31 | answer | added | David Feldman | timeline score: 4 | |
| Jul 7, 2010 at 21:23 | answer | added | Mariano Suárez-Álvarez | timeline score: 5 | |
| Jul 7, 2010 at 21:14 | answer | added | Bill Dubuque | timeline score: 2 | |
| Jul 3, 2010 at 19:02 | answer | added | Arturo Magidin | timeline score: 2 | |
| Jul 3, 2010 at 11:49 | history | edited | Willie Wong |
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| Jul 3, 2010 at 5:30 | comment | added | The Mathemagician | @Bjorn I think this question is really a general question about a proof technique. As such,it really should be tagged "mathematical logic" or "proof theory". "Set theory" can also be assigned,but it's less natural. | |
| Jul 3, 2010 at 4:25 | answer | added | Himanshu | timeline score: 0 | |
| Jan 21, 2010 at 12:38 | answer | added | Ravi Boppana | timeline score: 2 | |
| Jan 21, 2010 at 9:53 | answer | added | steve | timeline score: 0 | |
| Jan 19, 2010 at 3:04 | answer | added | Ravi Boppana | timeline score: 3 | |
| Jan 17, 2010 at 1:53 | answer | added | KConrad | timeline score: 19 | |
| Jan 17, 2010 at 1:39 | answer | added | Joel David Hamkins | timeline score: 28 | |
| Jan 17, 2010 at 0:43 | history | edited | Pete L. Clark |
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| Jan 17, 2010 at 0:39 | answer | added | François G. Dorais | timeline score: 3 | |
| Jan 17, 2010 at 0:12 | answer | added | Joel David Hamkins | timeline score: 7 | |
| Jan 16, 2010 at 23:49 | comment | added | Bjorn Poonen | @Pete: As for the combinatorics tag: I couldn't find a better one. I was thinking that "discrete math" might be appropriate, and combinatorics seemed to be closest to this. Feel free to re-tag the question. | |
| Jan 16, 2010 at 23:33 | comment | added | Bjorn Poonen | Yes, I'm aware of transfinite induction, but since the thrust of my question is the same in that setting as in the natural number setting, I phrased my question in the most elementary terms. | |
| Jan 16, 2010 at 23:11 | answer | added | Joel David Hamkins | timeline score: 11 | |
| Jan 16, 2010 at 23:03 | comment | added | Joel David Hamkins | Bjorn, this phenomenon is not limited to induction on the natural numbers, but arises naturally in transfinite recursion also. Indeed, it is usually considered a feature of a properly performed transfinite recursion if it has the property you state. Perhaps you want to generalize your question? | |
| Jan 16, 2010 at 22:15 | answer | added | Mike Shulman | timeline score: 5 | |
| Jan 16, 2010 at 13:37 | comment | added | Harry Gindi | Most uses of induction can be simplified to strong induction. Also, strong induction lets you generalize to the transfinite case without changing your approach. | |
| Jan 16, 2010 at 8:35 | comment | added | Kevin Buzzard | This comment is too facetious to be an answer, but you could let P(n) be the statement "P(t) is true for all 0<=t<n" ;-) | |
| Jan 16, 2010 at 7:34 | answer | added | Gerhard Paseman | timeline score: 0 | |
| Jan 16, 2010 at 6:57 | comment | added | Qiaochu Yuan | This question is related to the question of whether there are natural ways to extend the definition of a combinatorial sequence defined at the positive integers to 0 (which I asked about here: mathoverflow.net/questions/1176/…). I think this is what Bjorn is thinking about, anyway, because he gave a lecture on the subject once which is the reason I asked that question! | |
| Jan 16, 2010 at 6:47 | comment | added | Pete L. Clark | Interesting question. (I confess that, in the introduction to proofs class I taught twice in the last year, I didn't want to address the logical superfluity of the base case in strong induction for fear it would confuse my students. But I guess MIT students are not so easily confused.) Why is it tagged combinatorics? | |
| Jan 16, 2010 at 6:17 | comment | added | Bjorn Poonen | My first community wiki! I suppose I should remind everybody to include only one proof per answer. | |
| Jan 16, 2010 at 6:16 | history | asked | Bjorn Poonen | CC BY-SA 2.5 |