n-ary Symmetric Difference
As above, the symmetric difference of a collection of sets contains just elements which are in an odd number of the sets in the collection:
- .
Evidently, this is well-defined only when each element of the union is contributed by a finite number of elements of .
Suppose is a multiset and . Then there is a formula for, the number of elements in, given solely in terms of intersections of elements of :
- ,
where is meant to indicate that is a subset of distinct elements of, of which there are .
Read more about this topic: Symmetric Difference
Famous quotes containing the word difference:
“Life is a disease; and the only difference between one man and another is the stage of the disease at which he lives. You are always at the crisis: I am always in the convalescent stage.”
—George Bernard Shaw (1856–1950)