Countable Union of Countable Sets

[evinda]

Hello! (Wave)

I am looking at the proposition:

[m] If $(A_n)_{n \in \omega}$ is a sequence of sets and $(f_n)_{n \in \omega}$ is a sequence of functions then:

for all $n \in \omega, f_n: \omega \overset{\text{ surjective }}{\rightarrow} A_n$ then there is a function $f: \omega \overset{\text{ surjective }}{\rightarrow} \bigcup_{n \in \omega} A_n$. [/m]Could you give me an example of such a case?

 

[Evgeny.Makarov]

This simply says that the union of countably many sets that are at most countable is at most countable.

 

[evinda]

This simply says that the union of countably many sets that are at most countable is at most countable.

I see... Thanks a lot! (Smile)