Meaning of countable in definitions of sigma algebra

[Rasalhague]

Meaning of "countable" in definitions of sigma algebra

In the third axiom defining a $\sigma$-algebra, $(X,\Sigma)$, does countable mean (a) "finite or countably infinite", or does it mean (b) "countably infinite".

 

[mathman]

In this context it means (a), i.e. every countable(finite or countably infinite) union or intersection of sets in Σ is in Σ.

 

[Rasalhague]

Thanks.

 

[g_edgar]

In this context it means (a), i.e. every countable(finite or countably infinite) union or intersection of sets in Σ is in Σ.

I agree. But in this case (because the empty set is already there) it doesn't matter. A finite union is the same as a countably infinite union by appending empty sets to the list.