Timeline for Value of "of course" in the mathematical literature
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
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| Aug 24, 2010 at 19:02 | comment | added | Andreas Blass | @Mariano: In some cases, "by definition" serves as a useful substitute for "obviously." It tells the reader that what follows is easy to see and not to waste time trying to infer it from the technical lemmas he's just read --- simply go back to the definition. It's surprisingly easy to get so engrossed in technical lemmas that one doesn't think to look back at the definition until one is reminded to do so. | |
| Feb 24, 2010 at 5:25 | comment | added | Pete L. Clark | OK, I get it now: thanks for the explanation. As a sentence in a math book though I find it completely unobjectionable. (Certainly compared to the title: Basic Algebra II!) Anyway, the English word "irreducible" is not much used out of mathematics (possible exception: the recently popular phrase "irreducible complexity"): c.f. merriam-webster.com/dictionary/irreducible, where already the first definition alludes to mathematical ideas. | |
| Feb 24, 2010 at 3:29 | comment | added | Mariano Suárez-Álvarez | I tend not to like "By definition..." because everything is follows from the definitions... | |
| Feb 24, 2010 at 1:47 | comment | added | Ben Webster♦ | It might have been more helpful to say "By definition, every irreducible module is completely reducible." | |
| Feb 24, 2010 at 1:39 | history | made wiki | Post Made Community Wiki by Ben Webster♦ | ||
| Feb 24, 2010 at 1:00 | comment | added | Cory Knapp | I read the "of course" in that sentence to be something to counter what was said previously: "(Some statement about irreducible modules); of course [i.e. however,], every irreducible module is completely reducible. | |
| Feb 24, 2010 at 0:54 | comment | added | Douglas Zare | It's still a possible source of confusion worth a remark. Btw, "flammable" is a corruption of "inflammable." Clearer examples include that we park on driveways and drive on parkways, and that many words are their own opposites, like the verbs "table," "cleave," and "sanction." | |
| Feb 24, 2010 at 0:12 | comment | added | Qiaochu Yuan | But statements like that can be true in ordinary English. To wit: inflammable objects are often completely flammable. | |
| Feb 24, 2010 at 0:04 | comment | added | Douglas Zare | @Pete Read it in English as he suggests. "Not reducible at all implies very reducible" seems like nonsense. Obviously, that's not a good translation of the technical meaning, but imagine that you flip the book open to that statement first. | |
| Feb 23, 2010 at 23:45 | comment | added | Pete L. Clark | I don't get it -- it is true that every irreducible module is completely reducible and this immediate from the definition. What's the problem? | |
| Feb 23, 2010 at 23:16 | history | answered | Scott Carter | CC BY-SA 2.5 |