Timeline for Examples of common false beliefs in mathematics
Current License: CC BY-SA 2.5
21 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 21, 2019 at 11:02 | comment | added | Hollis Williams | The terminology is unfortunate, but it's very easy to see that a set can be both open and closed, if you show that to someone the terminology should be clear. | |
| Apr 8, 2019 at 8:53 | comment | added | Toby Bartels | @N Unnikrishnan : Yes, and in this analogy, the doors are quite explicitly the points of the boundary. | |
| Aug 8, 2017 at 2:48 | comment | added | Integral | The terminology is poor, let it be doors or rooms or whatever. It's common sense that objects which can be open or close, usually are in only one of these states: doors, chests, safes, lockers, etc. These words are considered opposites! It's like define some sets to be hot and cold and then say there are some sets which are hot and cold at the same time. Please, if this is the case, just don't use these words. Good notation and good terminology are important. | |
| Jul 24, 2017 at 10:32 | comment | added | N Unnikrishnan | To all the people who find fault with topologists' terminology, sets should be compared with rooms, not doors in the first place, should they not? And the room analogy fits this bill well - rooms can be open, closed, partially open or partially closed to any degree. | |
| Dec 7, 2016 at 1:05 | comment | added | Danu | @Ovi No, that is not right. The student said: The set is open, hence not closed." This is wrong because there are sets which are open and closed, not because there are sets that are neither. For instance, in $\Bbb R$ (equipped with its standard topology), the sets $\Bbb R$ and $\varnothing$ (the second is the empty set) are both open and closed. In fact, they are the only open and closed sets in $\Bbb R$, since $\Bbb R$ is connected. | |
| Aug 19, 2016 at 15:06 | comment | added | Ovi | @NateEldredge Sorry, I am just an undergrad student reading this out of interest. I want to make sure I know where the mistake is here: An open set is $(2, 4)$, a closed set is $[2, 4]$, but the student failed to take into account sets such as $(2, 4]$ and $[2, 4)$, which are neither open nor closed? | |
| Jan 28, 2012 at 16:45 | comment | added | Todd Trimble♦ | See also arsmathematica.net/archives/2012/01/20/hitler-on-topology | |
| Apr 14, 2011 at 19:24 | comment | added | roy smith | I think we need more detail to be fair. Was this afternoon's student perhaps contemplating a non empty proper subset of R? | |
| Jun 7, 2010 at 18:11 | comment | added | Terry Tao | The mere existence of the adjective "half-open", as in "the half-open interval [1,2)", is a fairly good antidote to this, even if the notion of half-openness per se does not extend particularly well beyond the interval case. | |
| Jun 6, 2010 at 11:46 | comment | added | Henno Brandsma | Actually, topologists have studied spaces where every set is open or closed (or both, of course), and they're called "Door spaces".... | |
| Jun 5, 2010 at 22:47 | comment | added | Josh | When is a set not a set? | |
| May 31, 2010 at 8:03 | comment | added | Michael Hoffman | I like that "Sets are not doors", I can say that I have thought too fast and made this assumption and ended up proving something that couldn't possibly be true >< | |
| May 26, 2010 at 22:52 | comment | added | hypercube | On my office door I once put "clopen the door" | |
| May 21, 2010 at 15:23 | comment | added | Pietro Majer | some students are a rich source of false beliefs. Try asking whether the product of two odd functions on R is odd or even. | |
| May 6, 2010 at 2:17 | comment | added | jeremy | So are you saying sets are closed, open, clopen, or ajar? ;) | |
| May 5, 2010 at 21:52 | comment | added | CrazyHorse | On the other hand, one can say "open the door" and "close the door" in reference to a door that is slightly ajar. | |
| May 5, 2010 at 20:53 | comment | added | Qiaochu Yuan | Munkres is fond of saying "sets are not doors." | |
| May 5, 2010 at 20:25 | comment | added | Kevin Buzzard | Either that or topologists need a sit-down about the facts of life in life, where they are told how unfortunate their notation is... | |
| May 5, 2010 at 16:56 | comment | added | The Mathemagician | Yikes,that student needs a sit-down about the facts of life in topology. | |
| May 5, 2010 at 14:39 | comment | added | Nate Eldredge | The terminology is rather unfortunate. | |
| May 5, 2010 at 13:18 | history | answered | Alekk | CC BY-SA 2.5 |