Timeline for What is your favorite "strange" function?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Apr 29, 2021 at 15:37 | comment | added | user147820 | @DanielMiller now I'm being a bit pedantic, for which I apologize, but I think it should be $2^{\aleph_0}$, unless we're assuming the continuum hypothesis. anyway +1, I agree this isomorphism is a very bizarre function indeed! | |
| Dec 12, 2020 at 18:59 | comment | added | Daniel Miller | You're right. The subscript should be $\aleph_1$. | |
| Dec 11, 2020 at 2:48 | comment | added | user147820 | @DanielMiller perhaps I'm being dense, but surely $S^1$ is not isomorphic to $\mathbb{Z}/\mathbb{Q}\times\bigoplus_\omega\mathbb{Q}$? the former is uncountable, but the latter is a cartesian product of two countable sets and is hence countable. ($\bigoplus_\omega\mathbb{Q}$ is the set of functions from $\omega$ to $\mathbb{Q}$ with finite support) | |
| Jul 17, 2012 at 11:56 | comment | added | Daniel Miller | The proof of their existence comes from the structure theorem for divisible abelian groups. Both are isomorphic to $\mathbb{Z}/\mathbb{Q}\times \bigoplus_\omega \mathbb{Q}$. | |
| Jul 17, 2012 at 7:31 | comment | added | Bernikov | Could you please give an example of such an isomorphism, or at least an argument to prove that these groups are isomorphic? I find it quite surprising. | |
| Aug 21, 2010 at 18:31 | history | answered | Daniel Miller | CC BY-SA 2.5 |