A ring is closed under intersection. And delta-ring is closed under countable intersection. According to my understanding, if a family of sets is closed under intersection, than it should also be closed under countable intersection.

Let's say $R$ is a ring. To $R$ be a delta-ring, ${A}_{n}\cap {A}_{n+1}\cap {A}_{n+2}\cap ...$ should also be in $R$. And, as a ring is closed under intersection, ${A}_{n}\cap {A}_{n+1}$ is in $R$, then ${A}_{n}\cap {A}_{n+1}\cap {A}_{n+2}$ is in $R$, and so on. So, any ring is a delta-ring.

What am I missing? I guess I don't properly understand what countable intersection is. Thank you for reading!

Let's say $R$ is a ring. To $R$ be a delta-ring, ${A}_{n}\cap {A}_{n+1}\cap {A}_{n+2}\cap ...$ should also be in $R$. And, as a ring is closed under intersection, ${A}_{n}\cap {A}_{n+1}$ is in $R$, then ${A}_{n}\cap {A}_{n+1}\cap {A}_{n+2}$ is in $R$, and so on. So, any ring is a delta-ring.

What am I missing? I guess I don't properly understand what countable intersection is. Thank you for reading!