Timeline for What are good ways to present proofs of theorems requiring auxiliary lemmas? [closed]
Current License: CC BY-SA 3.0
20 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 1, 2015 at 16:34 | review | Reopen votes | |||
| Aug 1, 2015 at 20:24 | |||||
| Sep 11, 2013 at 13:04 | review | Reopen votes | |||
| Sep 11, 2013 at 13:06 | |||||
| Aug 6, 2013 at 17:58 | vote | accept | I Like to Code | ||
| Aug 2, 2013 at 12:03 | comment | added | M.G. | For what it's worth, here is my perspective of a graduate student: if there is nothing wrong with lemma -> proof of lemma -> theorem -> proof of theorem, then there is no need to make things more complicated for the reader than they already are, by nesting stuff. Unless it is an overview of a result, a proof should follow the statement immediately.The reader can always skip lemma/corollary/proof on his own if he wishes to do so, so there is hardly any need to break logical flow. Everything else is just friggin' annoying to read and understand! | |
| Aug 2, 2013 at 4:19 | comment | added | Peter Samuelson | It can be helpful to the reader (or at least to me) to have the statement of the theorem appear before technical lemmas that are used in the proof. It's irritating to have to flip through some pages of before seeing the statement they're used to prove. So I would go for the second method, in general. | |
| Aug 2, 2013 at 2:55 | comment | added | Emerton | Dear Coder, I prefer to adopt the second style, rather than having nested proofs, for reasons similar to darij's: the hypotheses in force at any point become clearer, and also the logical flow is easier for the reader. Regards, | |
| Aug 2, 2013 at 2:28 | history | edited | I Like to Code | CC BY-SA 3.0 |
improved phrasing of question in title
|
| Aug 2, 2013 at 0:35 | history | closed |
Daniel Moskovich BS. John Pardon Andy Putman Gerald Edgar |
Opinion-based | |
| Aug 2, 2013 at 0:30 | comment | added | Amir Asghari | The first way has a more educational flavor that is going better with the flow of thinking. It is like saying that "now, it is enough to show that..."; and that is your lemma. | |
| Aug 2, 2013 at 0:28 | answer | added | MTS | timeline score: 6 | |
| Aug 2, 2013 at 0:19 | comment | added | Noah Schweber | I think this question is too localized for MO as phrased currently, but that doesn't make MSE a better fit. A better way to phrase it might be, "What are good ways to present proofs of theorems requiring auxiliary lemmas?" Certainly, though, this question is of interest to research mathematicians, and is specifically about mathematical writing. | |
| Aug 2, 2013 at 0:14 | review | Close votes | |||
| Aug 2, 2013 at 0:39 | |||||
| Aug 2, 2013 at 0:11 | history | edited | Ricardo Andrade |
added relevant tags
|
|
| Aug 2, 2013 at 0:08 | comment | added | darij grinberg | +1 for asking such a question, although I understand the close voters: such a question might be better at math.stackexchange. | |
| Aug 2, 2013 at 0:07 | comment | added | John Pardon | Obviously which is more natural / easier to read depends a lot on the specific context (for example, the relative length of the proof of the theorem and/or lemma, and whether the lemma is really just a "claim" on the way to proving the theorem or rather more independent). | |
| Aug 2, 2013 at 0:07 | comment | added | darij grinberg | I agree that the second way is better. The first way leaves the question unanswered whether the lemma is only formulated in the context of the theorem, in the context of its proof (which may be more restrictive, e. g., due to WLOG assumptions or cases) or in the context of the surrounding paper. In the second way, it is clear that the context is that of the surrounding paper. | |
| Aug 1, 2013 at 23:59 | review | First posts | |||
| Aug 2, 2013 at 0:07 | |||||
| Aug 1, 2013 at 23:59 | comment | added | Piyush Grover | Theorem--->lemma--->Proof-of-lemma---->proof of theorem. | |
| Aug 1, 2013 at 23:54 | comment | added | JRN | I more often see the order lemma, theorem, proof. | |
| Aug 1, 2013 at 23:40 | history | asked | I Like to Code | CC BY-SA 3.0 |