[chompychop]

The formal definition in the link makes this precise. Yes, 100 sets which are pairwise disjoint (which makes any pairwise intersection empty) would make a sunflower. Your second example is not a sunflower, because the definition requires that if you take the intersection of any two sets from those 100, the resulting set should be the same. So if you pairwise take those sets with unique elements, you get the empty set as intersection, but if you pairwise take two sets with shared elements, you get a set of the shared elements as intersection. The pairwise intersection should always be the same for it to be a sunflower. And yes, a collection of two sets would always be a sunflower.

[holden_nelson]

I read the second example as: every set contains some elements that are totally unique to that set, and also some elements that are common to all of the sets, and nothing else. So I think it is a sunflower - any pairwise intersection just has the shared elements.

e.g 100 sets of integers, of size 3. Each set contains a unique number from 1-100, and every set also contains 1000 and 10000. Any pairwise intersection is {1000, 10000}.