Timeline for "Let $x \in A$", beginning a proof of "$\forall x \in A$ ...", if A were empty [closed]
Current License: CC BY-SA 2.5
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 23, 2010 at 17:59 | comment | added | Alexander Woo | Is there an underlying tension between platonists and formalists here, or am I reading into things? | |
| Nov 23, 2010 at 16:52 | comment | added | Thierry Zell | As pointed out already, the empty case deserves careful treatment. I do find it incredible however that this would be one of the big issues arising in teaching. I don't want to cast blame without more context, but it does make your colleagues look good. | |
| Nov 23, 2010 at 16:29 | comment | added | arsmath | I don't see why this is off-topic. You have a point that actual professors at a four-year college are confused about. What better place for him or her to turn than here? | |
| Nov 23, 2010 at 16:25 | comment | added | Willie Wong | Casting the final vote based on Todd's first comment. Questions 2 and 3 are inappropriate for MO, while question 1 you probably already know how to address (if not, see the many answers already given below). | |
| Nov 23, 2010 at 16:23 | history | closed |
Todd Trimble José Figueroa-O'Farrill Robin Chapman Andrés E. Caicedo Willie Wong |
off topic | |
| Nov 23, 2010 at 16:04 | answer | added | arsmath | timeline score: 8 | |
| Nov 23, 2010 at 14:03 | answer | added | Andrej Bauer | timeline score: 25 | |
| Nov 23, 2010 at 13:47 | comment | added | Deane Yang | I vote for Todd's second response, but this has to be done with care. You don't want to send students out spending too much time thinking and talking about the empty set. But they should know that it can be an issue and therefore should be considered in advance. It is well-known that a certain mathematician currently living in France has flustered many a speaker by simply asking "but what about the empty set?" after a theorem has been stated. | |
| Nov 23, 2010 at 13:45 | answer | added | Nate Eldredge | timeline score: 11 | |
| Nov 23, 2010 at 13:44 | answer | added | Andreas Blass | timeline score: 5 | |
| Nov 23, 2010 at 13:34 | answer | added | Stefan Geschke | timeline score: 7 | |
| Nov 23, 2010 at 13:31 | comment | added | Todd Trimble | However, to temper my withering contempt just a bit: it's really not a bad idea to get into (and teach your students) the habit of thinking about the empty case, because even grown mathematicians slip up here. An example might be: how many connected components does the empty space have? | |
| Nov 23, 2010 at 13:18 | comment | added | Todd Trimble | I think you're right, but we don't handle social questions here, so I'm afraid this question is off-topic. I'll say that I think this sort of objection is very picayune and without merit if it is raised each and every time -- one dispenses with such things in the first week of class and it "goes without saying" henceforth. Aiming for clarity and naturalness of expression is much more important than satisfying the petty-minded demands of pedantic colleagues. | |
| Nov 23, 2010 at 13:06 | history | asked | Coward | CC BY-SA 2.5 |