Timeline for Examples of interesting false proofs
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 15, 2021 at 22:02 | comment | added | Alessandro Della Corte | A nice realization of a counterexample can be the relation: "to love someone". In an ideal world, symmetry and transitivity of this relation should hold. But everyone knows that you can't really love yourself if no one loves you... | |
| Mar 31, 2020 at 19:45 | comment | added | Dan Petersen | @trisct It is a fallacy since $H=\varnothing$ is closed under multiplication and inverses, but is not a subgroup; in this case the first step "take any $x \in H$" fails. | |
| Dec 27, 2019 at 5:14 | comment | added | trisct | @DanPetersen Interesting. How is this a fallacy? | |
| Jan 10, 2019 at 17:10 | comment | added | Dan Petersen | A very similar fallacy: a subset $H$ of a group $G$ is a subgroup if it contains the unit, is closed under multiplication, and is closed under inverses. CLAIM: the second and third condition imply the first. Indeed, take any $x\in H$. Then $x^{-1}$ is also in $H$, so $xx^{-1}=e$ is in $H$. | |
| Mar 20, 2013 at 20:33 | comment | added | Paul Levy | As Davidac says you only need that for any $x$ there exists at least one $y$ such that $x \sim y$. I set this as a homework question for my undergraduate groups course every year and the answers systematically ignore the necessary assumption | |
| Mar 20, 2013 at 18:02 | comment | added | David Corwin | But this proves the result if there is at least one equivalence? | |
| May 19, 2012 at 18:06 | history | answered | John Engbers | CC BY-SA 3.0 |