Talk:Countable Union of Finite Sets is Countable

merge request
No. ACC for finite sets is a weaker choice principle than ACC.

ACC for finite sets is equivalent to the countable union condition for finite sets.

ACC is not equivalent to the countable union condition. --Dfeuer (talk) 06:59, 9 May 2013 (UTC)


 * This information is not much use in the context of a talk page. The site might benefit from the distinction being made on the pages in question. --prime mover (talk) 07:53, 9 May 2013 (UTC)

Definition of $h$
Regarding the current Explain tag: I'm unsure whether the question is rhetorical, so for the benefit of other readers I'll treat it as if it weren't. The meaning of this concatenation is evaluation of the function $q \left( {g_1 \left( {n} \right)} \right)$, which is itself a bijection from $|f \left({g_1 \left( {n} \right)}\right)|$ to $f \left({g_1 \left( {n} \right)}\right)$, at the point $g_2 \left({n}\right)$. By construction of $g$, $g_1$ is the index of a member $F$ of $\mathcal F$, and $g_2$ is the index of an element of $F$.

I would add this explanation to the text, but I'll leave this to a user more experienced with ProofWiki's style guides. Jumpythehat (talk) 21:54, 2 October 2020 (UTC)