I've always had the following silly(?) doubt about convergent sequences.
Given a finite sequence $A_{1:n}=(a_1,a_2\ldots ,a_n)$, define its reverse as $rev(A) = (a_n,a_{n-1},..a_1)$. Further, if $A$ is infinite, define its reverse as the limit of the reverses of its initial subsequences, i.e. as the limit of the sequence of sequences $ \{ (a_1), (a_2,a_1), (a_3,a_2,a_1), ..\}$.
Q: Is this notion well defined? Why or why not?
I suspect not, because the reverse of $(1,\frac{1}{2},\frac{1}{3},...)$ would be $(0,0,... , \frac{1}{3},\frac{1}{2},1)$? This seems absurd!