Timeline for Examples of common false beliefs in mathematics
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Dec 1, 2010 at 15:30 | comment | added | Peter LeFanu Lumsdaine | Hmm, very nice (once clarified to the open ball)! Easily dispelled as soon as you question it, but I could easily imagine using it without thinking and missing the alternation of quantifiers that’s going on under the surface. | |
| Dec 1, 2010 at 15:27 | history | edited | Peter LeFanu Lumsdaine | CC BY-SA 2.5 |
incorporated clarifications from comments
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| Oct 10, 2010 at 19:24 | comment | added | user4977 | You are right, I should have specified open ball, thanks. I think it is just barely false for the open ball. Honestly, I held this false belief until a couple of days ago, and I haven't thought much about correcting my belief. Probably the real open epsilon ball is the union of all functions that fit between dashed curves a distance strictly less than epsilon away from f? At any rate, I think the above picture is the right way to think about it most of the time. But it gives results such as $tan^{-1}$ being in the open ball of radious pi/2 centered at 0 if you interpret it literally. | |
| Oct 10, 2010 at 18:26 | comment | added | Nate Eldredge | Surely this is true if you are talking about the closed ball, and only just barely false for the open ball (and if we were talking about functions from $[a,b]$ to $\mathbb{R}$ it would be true)? Or else I am one of those with the false belief... | |
| Oct 9, 2010 at 20:00 | history | answered | user4977 | CC BY-SA 2.5 |