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8:07 AM
I am not sure whether this
5
Q: Evaluating the double limit $\lim_{m \to \infty} \lim_{n \to \infty} \cos^{2m}(n! \pi x)$

avz2611i have to find out the following limit $$\lim_{m\to\infty}\lim_{n\to\infty}[cos(n!πx)^{2m}]$$ for $x$ rational and irrational. for $x$ rational $x$ can be written as $\frac{p}{q}$ and as $n!$ will have $q$ as its factor the limit should be equal to 1. the second part of irrational is giving me pr...

should or should not be closed as a duplicate of this
8
Q: How to prove that $\lim(\underset{k\rightarrow\infty}{\lim}(\cos(|n!\pi x|)^{2k}))=\chi_\mathbb{Q}$

Steve Possible Duplicate: How is this called? Rationals and irrationals Please help me prove, that $$\underset{n\rightarrow\infty}{\lim}\left(\underset{k\rightarrow\infty}{\lim}(\cos(|n!\pi x|)^{2k})\right)=\begin{cases} 1 & \iff x\in\mathbb{Q}\\ 0 & \iff x\notin\mathbb{Q} \end{cases}$$ See...

(or some more suitable candidate for a duplciate).
I am not sure whether to read today question as How to prove this? or What is wrong with my approach?
8:30 AM
Ignore what I just wrote. They are different questions.
Doh'! I noticed only now that this is a different questions. Order of the limit is different. Your question is about $\lim_{m \to \infty} \lim_{n \to \infty} \cos^{2m}(n! \pi x)$, the questions I linked are about $\lim_{n \to \infty} \lim_{m \to \infty} \cos^{2m}(n! \pi x)$ — Martin Sleziak 43 secs ago
 
10 hours later…
6:11 PM
Okay, it seems I was wrong on a technicality. The description for the duplicate flag states "this question has been asked before and already has an answer", which didn't apply in my situation. The network meta question "How to handle a deliberate duplicate question" suggests that we (at least us <3k users) should just flag for moderator attention instead.

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