The post is wrong in saying that U contains only cofinite sets. It obviously must contain plenty of sets that are neither finite nor cofinite, because the complements of those sets are also neither finite nor cofinite. Possibly the author intended to type “contains all cofinite sets” instead.
Yep, this is correct! I’ve updated the post to reflect this.
E.g. if an ultrafilter contains the set of all even naturals, it won’t contain the set of all odd naturals, neither of which are finite or cofinite.
Yep, this is correct! I’ve updated the post to reflect this.
E.g. if an ultrafilter contains the set of all even naturals, it won’t contain the set of all odd naturals, neither of which are finite or cofinite.