Let $\{E_n\}$, $n = 1, 2, 3, \ldots$, be a sequence of countable sets, and put $S = \displaystyle \bigcup_{n=1}^{\infty} E_n$. Prove that $S$ is countable.
Asked
Active
Viewed 122 times
0
-
(Are we assuming the sets $E_n$ are all infinite? Otherwise, this is not quite a duplicate of the linked question.) – Andrés E. Caicedo Feb 06 '13 at 23:04
-
1@Andres: It appears to be quoted verbatim from Baby Rudin, which defines countable to mean countably infinite, so the assumption is probably justified. If not, this question covers the countably infinite union of non-empty finite sets. – Brian M. Scott Feb 06 '13 at 23:14