Let A be a set of all finite subsets of positive integers. I have proved closure and associativity under intersection. I am kind of confused about existence of identity. Originally, I was thinking that the set of all positive integers also lives in A and when any set M in A intersects with that set, we will get M back. However, I am not sure if the set of all positive integers even lives in A cause it is not finite, is it?
Any help would be great.