Timeline for Examples of common false beliefs in mathematics
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 30, 2021 at 16:46 | comment | added | Maximilian Janisch | As a simple example: Consider the (formal) polynomial $P(X)=X^2+X \simeq (0,1,1,0,0,\dots)\in\mathbb Z_2^{\mathbb N_0}$, which indeed satisfies $P(0)=P(1)=0$ in $\mathbb Z_2$. | |
| Oct 27, 2018 at 6:37 | comment | added | Kapil | I once heard this used to "prove" that $\mathbb{F}_2$ is algebraically closed. The "idea" is that any non-constant polynomial over this field "must" take a value different from 1. However, the only other value available is 0! | |
| Apr 22, 2016 at 8:20 | comment | added | Jose Brox | Also closely related: Fermat's Little Theorem can be used to prove equality of polynomials. E.g., $X^2=X$ in $\mathbb{Z}_2[X]$ because $x^2=x$ in $\mathbb{Z}_2$. | |
| Mar 10, 2016 at 4:49 | history | edited | Michael Hardy | CC BY-SA 3.0 | added 10 characters in body |
| Jun 8, 2010 at 0:04 | comment | added | Jacques Carette | This is another example of intension/extension (the distinction I was trying to get at in question mathoverflow.net/questions/18848/…). | |
| Jun 6, 2010 at 20:53 | comment | added | Vania Mascioni | This seems related to the widely held belief that 1+1=2, (and how could 2 be equal to 0 ?!). On a psychological level this may connect with the assumption we all tend to make that a is different from b when asked to count the elements of set {a,b} (a related entry is somewhere else on this page), or that in general two different symbols are instinctively taken to denote two distinct objects. | |
| Jun 6, 2010 at 18:37 | history | edited | Terry Tao | CC BY-SA 2.5 | deleted 21 characters in body |
| Jun 6, 2010 at 18:29 | history | answered | Terry Tao | CC BY-SA 2.5 |