Timeline for Terminology: A "corollary" to a proof?
Current License: CC BY-SA 4.0
7 events
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| S Jul 30 at 10:10 | history | suggested | CommunityBot | CC BY-SA 4.0 |
Touch up punctuation, especially "cumbersome-to-phrase", which is hard to parse without the hyphens
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| Jul 30 at 4:08 | review | Suggested edits | |||
| S Jul 30 at 10:10 | |||||
| Jul 29 at 17:38 | comment | added | Lee Mosher | In the situation you have presented, I would not leave it as just a remark. Instead, I would do something like this: "Examination of the proof shows that we have actually proved a stronger statement, with a weaker hypothesis: Theorem..." In order to do this it might also be necessary to export a definition or two from the proof to this post-proof position. I suppose a reader might wonder why the theorem was not stated like that in the first case, but as you say, there can be expository reasons for doing things that way, e.g. because the "weaker hypothesis" might be annoyingly technical. | |
| Jul 29 at 6:44 | comment | added | Peter Taylor | I have an example of this in a pre-print. The goal of the paper was to determine which abelian groups had a certain property. The proof ended up using a much weaker but more technical condition than "abelian group", and in particular worked for all quasigroups. My coauthor persuaded me that rewriting the whole paper in terms of quasigroups would obscure the original motivation, and we settled on a remark to the effect that the proof carried over to quasigroups, and perhaps the literature on related properties could be reexamined in that context. | |
| Jul 29 at 5:11 | comment | added | Kimball | @LSpice I've made remarks for things like this also, and I guess my philosophy is that it depends how important/useful it seems. | |
| Jul 28 at 22:58 | comment | added | LSpice | Ha, I commented "please, before the proof!" while reading the beginning, only to see at the end that my objection had been preëmpted. I do wonder to what extent you think that this kind of postscript is appropriate in, say, a textbook vs. a paper. (Personally, I think either one argues against it: in a textbook, one must be particularly gentle on readers who are new to the subject; whereas, in a paper, I am much more likely to read asynchronously, and so benefit from a note that will tell me how to dip into the proof before I dip into it, than to read it as one whole piece of exposition.) | |
| Jul 28 at 22:56 | history | answered | Sam Hopkins | CC BY-SA 4.0 |