I am thinking about a problem involving intersection of sets.
If I have for example a two sets A and B, and |A| is the number of elements in A and |B| the number of elements in B, then |A \cap B| is the number of elements in the intersection set A \cap B.
Now, if I add a third set C, with |C| elements, the number of elements in A \cap B \cap C will be naturally smaller (or equal) than in A \cap B. And if I'll add more sets, the number of elements in the intersection will keep decreasing.
Are there any researches / theorems about the rate of decrements ? I mean, if I take sets with numbers that are chosen by random, and I keep adding them, how strongly will the number of elements in the intersection converge to zero ?
Any insights / references will be most appreciated...
/cap means intersection, couldn't make latex work, don't know why...apologies...